I'll keep this one a bit shorter. Not going to worry about specific weapons, naturally legendary weapons break the game later on.
You mean a Hoopak? It's as legendary as a longsword. It's a traditional Kender weapon. I'm sure magical versions exist, but this is mundane. It's basically a staff sling but with a sharp point at the bottom; it's a spear that you can't throw with a sling on the other end of it. The basic sling is a "shepherd's sling".
I meant, there is no need to break down into every potential option for slings and quarterstaves. We can just stick with basic sling and quarterstaff for the comparison.
You said thirsting blade and devouring blade could not apply except for magical slings. That is not true because the Hoopak exists and can be summoned by Pact of the Blade. It's a Dragonlance item, but it's reasonable to adapt to other campaigns if your GM is okay with it. It should be available in a Planescape setting as well.
If every dungeon is a building with doors at every corner, then it's also an issue. Not all dungeons are the same, and spells are components for a reason, if the GM is handwaving these things every time, that is down to them but it's not how the rules have these things going down. Ultimately the whole "cast it before the battle" isn't applicable every time and the limited number of pebbles would heavily interfere with a class like Warlock when using spells like Hex.
Where exactly are the rules on how far away a verbal spell components can be heard? Please, provide the non-handwaved rule that provides a concrete definition of that range. Or how loud the verbal components are. Yeah, there are a lot of doors and with them a lot of checks for traps and other door routines. Hex use a Bonus Action to set the target and none to deal extra damage. In single encounters, you can get by with a single casting (or setting the target from a prior casting) and both Magic Stone and Polearm Master are unrestricted.
Crusher's 5 foot push is automatic 1 per turn, so long as the creature is not two sizes or more larger than you. Crusher's advantage is automatic on Critical but that is not a reliable way of getting advantage, there are other ways to get advantage which can be better from other classes and generally would not want to be relying on a Warlock for doing this. On top of this, PAM also gives an additional reaction, one that can trigger far easier than opportunity attacks normally would.
If you're getting 2+ attacks with a melee weapon, you aren't likely to trigger the Polearm Master reaction unless you lose initiative or the encounter has multiple melee enemies, but even then, it's likely once per encounter.
I forgot about the once per turn on Crusher. I was trying to figure out ways to trigger falling without Push mastery or Repelling Blast. If you can trigger the falling consistently, that is the reliable way to get advantage, not Enhanced Critical, not Topple. You can, however, use Crusher's Push to move an enemy through a Spike Growth, away from someone who just hit with Booming Blade. Topple's effectiveness will vary by enemy, but drops off unsurprisingly against higher CR enemies where advantage is more critical than against a cluster of lower CR opponents. Magic Stone is also nice because you don't have to invest any of the feats to maximize it. Bonus Action cast it on pebbles via your invisible familiar and you eldritch blast with your action. Your ally with the feat investments and weapon masteries actually does the stone toss. Or you just pass them out to someone who doesn't otherwise have an effective attack.
Shillelagh and Polearm Master don't really help with using Magic Stone with Agonizing Blast, though.
You said thirsting blade and devouring blade could not apply except for magical slings. That is not true because the Hoopak exists and can be summoned by Pact of the Blade. It's a Dragonlance item, but it's reasonable to adapt to other campaigns if your GM is okay with it. It should be available in a Planescape setting as well.
You or someone else can make a ranged spell attack with one of the pebbles by throwing it or hurling it with a sling.
Where permits anything but a sling in the magic stone spell itself? If you threw a magic stone with a catapult, it would not activate the spell effect on the stone since the spell does not permit that.
So either A, the Hoopak counts as a sling, it is a sling and can be used as a sling or B the Hoopak acts as sling but is not a sling itself, it can not be used as a sling for the magic stone spell. Either way what I said about a sling remain true, this is no different from how Shillelagh can only be cast on clubs or quarterstaffs, and oh, you can cast shillelagh on a staff since a staff can be used as a quarterstaff? yes or no? if yes, well it's because a staff is also a quarterstaff.
Where exactly are the rules on how far away a verbal spell components can be heard? Please, provide the non-handwaved rule that provides a concrete definition of that range. Or how loud the verbal components are. Yeah, there are a lot of doors and with them a lot of checks for traps and other door routines. Hex use a Bonus Action to set the target and none to deal extra damage. In single encounters, you can get by with a single casting (or setting the target from a prior casting) and both Magic Stone and Polearm Master are unrestricted.
Verbal (V)
A Verbal component is the chanting of esoteric words that sound like nonsense to the uninitiated.
If Verbal components can't be heard, then why do they sound like nonsense to the uninitiated? Clearly they are audible, it is also clearly stated they are chants after all. Additionally for the very purpose of avoiding this, the Subtle Spell metamagic exists, if the DM isn't checking if things can hear you then they are basically giving you a class feature for free.
It is up to the DM to determine how far it goes, additionally how different creatures would perceive it, that is why there is no hard and vast rule but if somebody is casting a spell 1 room over and there is no other sound, it'll be audible to the average human, to some creatures it may even be audible 1/2 rooms over, something like a Blink Dog might hear you two rooms over while that same Blink Dog might not hear a thing if the room has a waterfall in it. So it's situational however clearly, any verbal spell without the benefit of Subtle Spell can be counter spelled, 60 foot. So that's a good minimum over how far a spell can be heard audibly enough to be counter spelled, even when there is a waterfall in the room, it's still 60 foot.
If you're getting 2+ attacks with a melee weapon, you aren't likely to trigger the Polearm Master reaction unless you lose initiative or the encounter has multiple melee enemies, but even then, it's likely once per encounter.
There are multiple ways with warlock to get them multiple times per encounter actually, the easiest is to get weapon mastery feat and wield a Pike, you push the creature back 10 foot, it has to run back into range if it's melee and re-triggers the attack.
Now with Shillelagh, if you topple the creature, you can also just walk out of range.
You might intentionally trigger opportunity attacks if you're using Armor of Agathys to proc more damage output, tho that does risk concentration checks if using a concentration spell.
There is also mixing in Eldritch Blast with Repelling Blast and spell sniper to create distance. Having Devil's sight and using darkness, gives advantage against a lot of foes and you can not opportunity attack what you can not see... so plenty of ways for a Warlock to do this.
You can, however, use Crusher's Push to move an enemy through a Spike Growth, away from someone who just hit with Booming Blade. Topple's effectiveness will vary by enemy, but drops off unsurprisingly against higher CR enemies where advantage is more critical than against a cluster of lower CR opponents.
The push is 5 foot, you'd do more just using a pike with weapon master or hitting with repelling blast, here Crusher is just pointless, Topple is still better and has no size limitation like Crusher does, where Crusher quickly loses it's only consistent perk. If you're getting Crusher then really, you're going for a Crit fishing build to be triggering the advantage a lot, whereas Warlock simply doesn't have that. A Raging Barbarian, A Champion Fighter or An Oath of Vengance Paladin meanwhile can potentially get a lot of critical hits . It's really not the feat I would select for this build, unless you're really after constitution and for some reason resilient (constitution) isn't an option for you.
Magic Stone is also nice because you don't have to invest any of the feats to maximize it. Bonus Action cast it on pebbles via your invisible familiar and you eldritch blast with your action. Your ally with the feat investments and weapon masteries actually does the stone toss. Or you just pass them out to someone who doesn't otherwise have an effective attack.
Shillelagh and Polearm Master don't really help with using Magic Stone with Agonizing Blast, though.
I would say that Agonizing Blast isn't applicable to Magic Stone for the exact same reasons that Agonizing Blast isn't applicable to Shillelagh, so either they both get it or neither, and I'd say with how Agonizing Blast is written, it's neither.
Most people aren't going to put a weapon mastery into Sling, it's really for Niche situations where your STR based front-liners don't have long ranged attacks, you can help them do a bit more damage but for a Barbarian, it's an attack they do not use Strength (so not applicable to range) and for Paladin it's a ranged attack (so anything reliant on melee isn't working). It just changes very sub-par ranged damage to just being sub-par ranged damage. Now for the Paladin, there is a few ways to get some cantrip of their own and those cantrips will just be better, for the barbarian, they can reckless attack to throw javelins up to 120 foot with normal attacks, so it's really down to fighter or paladins that haven't got a charisma based ranged cantrip.
You said thirsting blade and devouring blade could not apply except for magical slings. That is not true because the Hoopak exists and can be summoned by Pact of the Blade. It's a Dragonlance item, but it's reasonable to adapt to other campaigns if your GM is okay with it. It should be available in a Planescape setting as well.
Where exactly are the rules on how far away a verbal spell components can be heard? Please, provide the non-handwaved rule that provides a concrete definition of that range. Or how loud the verbal components are. Yeah, there are a lot of doors and with them a lot of checks for traps and other door routines. Hex use a Bonus Action to set the target and none to deal extra damage. In single encounters, you can get by with a single casting (or setting the target from a prior casting) and both Magic Stone and Polearm Master are unrestricted.
If you're getting 2+ attacks with a melee weapon, you aren't likely to trigger the Polearm Master reaction unless you lose initiative or the encounter has multiple melee enemies, but even then, it's likely once per encounter.
I forgot about the once per turn on Crusher. I was trying to figure out ways to trigger falling without Push mastery or Repelling Blast. If you can trigger the falling consistently, that is the reliable way to get advantage, not Enhanced Critical, not Topple. You can, however, use Crusher's Push to move an enemy through a Spike Growth, away from someone who just hit with Booming Blade. Topple's effectiveness will vary by enemy, but drops off unsurprisingly against higher CR enemies where advantage is more critical than against a cluster of lower CR opponents. Magic Stone is also nice because you don't have to invest any of the feats to maximize it. Bonus Action cast it on pebbles via your invisible familiar and you eldritch blast with your action. Your ally with the feat investments and weapon masteries actually does the stone toss. Or you just pass them out to someone who doesn't otherwise have an effective attack.
Shillelagh and Polearm Master don't really help with using Magic Stone with Agonizing Blast, though.
How to add Tooltips.
My houserulings.
Where permits anything but a sling in the magic stone spell itself? If you threw a magic stone with a catapult, it would not activate the spell effect on the stone since the spell does not permit that.
So either A, the Hoopak counts as a sling, it is a sling and can be used as a sling or B the Hoopak acts as sling but is not a sling itself, it can not be used as a sling for the magic stone spell. Either way what I said about a sling remain true, this is no different from how Shillelagh can only be cast on clubs or quarterstaffs, and oh, you can cast shillelagh on a staff since a staff can be used as a quarterstaff? yes or no? if yes, well it's because a staff is also a quarterstaff.
If Verbal components can't be heard, then why do they sound like nonsense to the uninitiated? Clearly they are audible, it is also clearly stated they are chants after all. Additionally for the very purpose of avoiding this, the Subtle Spell metamagic exists, if the DM isn't checking if things can hear you then they are basically giving you a class feature for free.
It is up to the DM to determine how far it goes, additionally how different creatures would perceive it, that is why there is no hard and vast rule but if somebody is casting a spell 1 room over and there is no other sound, it'll be audible to the average human, to some creatures it may even be audible 1/2 rooms over, something like a Blink Dog might hear you two rooms over while that same Blink Dog might not hear a thing if the room has a waterfall in it. So it's situational however clearly, any verbal spell without the benefit of Subtle Spell can be counter spelled, 60 foot. So that's a good minimum over how far a spell can be heard audibly enough to be counter spelled, even when there is a waterfall in the room, it's still 60 foot.
There are multiple ways with warlock to get them multiple times per encounter actually, the easiest is to get weapon mastery feat and wield a Pike, you push the creature back 10 foot, it has to run back into range if it's melee and re-triggers the attack.
Now with Shillelagh, if you topple the creature, you can also just walk out of range.
You might intentionally trigger opportunity attacks if you're using Armor of Agathys to proc more damage output, tho that does risk concentration checks if using a concentration spell.
There is also mixing in Eldritch Blast with Repelling Blast and spell sniper to create distance. Having Devil's sight and using darkness, gives advantage against a lot of foes and you can not opportunity attack what you can not see... so plenty of ways for a Warlock to do this.
The push is 5 foot, you'd do more just using a pike with weapon master or hitting with repelling blast, here Crusher is just pointless, Topple is still better and has no size limitation like Crusher does, where Crusher quickly loses it's only consistent perk. If you're getting Crusher then really, you're going for a Crit fishing build to be triggering the advantage a lot, whereas Warlock simply doesn't have that. A Raging Barbarian, A Champion Fighter or An Oath of Vengance Paladin meanwhile can potentially get a lot of critical hits . It's really not the feat I would select for this build, unless you're really after constitution and for some reason resilient (constitution) isn't an option for you.
I would say that Agonizing Blast isn't applicable to Magic Stone for the exact same reasons that Agonizing Blast isn't applicable to Shillelagh, so either they both get it or neither, and I'd say with how Agonizing Blast is written, it's neither.
Most people aren't going to put a weapon mastery into Sling, it's really for Niche situations where your STR based front-liners don't have long ranged attacks, you can help them do a bit more damage but for a Barbarian, it's an attack they do not use Strength (so not applicable to range) and for Paladin it's a ranged attack (so anything reliant on melee isn't working). It just changes very sub-par ranged damage to just being sub-par ranged damage. Now for the Paladin, there is a few ways to get some cantrip of their own and those cantrips will just be better, for the barbarian, they can reckless attack to throw javelins up to 120 foot with normal attacks, so it's really down to fighter or paladins that haven't got a charisma based ranged cantrip.