With the light weapon rules of 2024, especially if using a vex and Nick weapon, you are better off as a melee ranger than as a ranged ranger. At levels 1-4 the light weapon melee ranger will hit at least once 88% of the time (0.8775) while the ranged, after L2 with archery style, has a 75% chance to hit (assuming the base chance is 0.65). If we move up to L5+ we have to include at least the possibility of dual wielding for the melee ranger giving them a possible 4 attacks to the ranged ranger’s 2.  For the ranged ranger the chance to get at least 1 hit is 94% while the chance to get both is 56%. For the melee ranger the chance for at least one hit out of their base 3 is 96%. For getting 2 out of their three it’s  72% and if you have 4 attacks thanks to dual wielding the chance to hit 3 out of 4 is still 55%  to me this seems very clear - in terms of base damage dealt the melee ranger has it all over the ranged ranger’s at basically every level. The only time the ranged PC gets results like melee is if your wielding 2 hand crossbows and have the xbow expert feat so you can ignore the loading property.But doing that basically moves you into melee range (30’). I can see picking up archery style with a later asi for ranged attacks from distance.

I don't have the math, but from watching optimization build videos for years, I know that the 2014 rules favored ranged combat in general- mostly due to the Sharpshooter and Crossbow Expert feats. I think that WotC was right to try to rebalance melee vs ranged martial combat, however, I also think they may have tipped the scales a bit too far in favor of melee. This is due mainly to the changes to the Great Weapon Master feat- which still adds a damage bonus to melee (albeit with heavy weapons only) and changes to the Sharpshooter feat- which has no damage bonus now.

In theory, ranged combat has defensive advantages of positioning, movement, and possibly even cover. But I don't think those advantages are actually realized often enough to validate the nerf that Sharpshooter got in 2024. I believe that many combats happen indoors- in some kind of room, hallway, cavern, etc. And that can limit or eliminate any positioning advantages from ranged combat. 

The Hunter's Mark spell/feature adds to the melee damage advantage over ranged, if the Ranger employs two weapon fighting- as you've pointed out. This is due to the nature of (sorry, bad pun) the Hunter's Mark spell. Because it adds damage to every hit, optimization pushes players towards getting the most hits possible- which is achieved by having the most chances to hit possible (i.e. number of attacks). 

It IS possible to get GWM on a longbow, but it's not easy because of the Strength requirement and the stat boost to Strength that the feat gives. Ranged combatants will want to focus on Dexterity. Maybe lucky stat rolls would make this easier. But if you're using Standard Array or Point Buy, spreading your points into Strength can be painful. (Rangers, of course, having Wisdom, Constitution,  and Dexterity [for ranged] as priorities.)

I think it might have been better for balance and for more viable playstyle choices if WotC had pursued one of the changes to Hunter's Mark proposed in one of the UA's. Specifically, there was a version that gave a d6 only once per turn, but upcasting the spell gave additional d6's. I think that is flawed, however. It should progress with Ranger Level, instead of spell level. This would help to avoid multiclass shenanigans. It could add another d6 at each of the "cantrip level ups" for Ranger levels (2d6 at 5th, 3d6 at 11th, 4d6 at 17th).  Or, some other progression perhaps. The once per turn limitation would make it an equal choice, no matter what kind of combat a player pursues- ranged, great weapon, sword/board, two weapon, etc. 

I'm not sure if Sharpshooter should have a damage bonus (which it does not, in 2024 rules). I think it's probably a good idea to incentivize heavy weapons, because players have to sacrifice defense (the option to use a shield). That being said, I think that maybe the Sharpshooter feat could live up to its name more than it does. The melee shooting, no disadvantage long range, and ignoring cover are fine. But I think it'd be cool if it did something like give players a bonus to hit (something flat, like a +1). And after level 5's multi-attack comes online, it could offer an option to sacrifice one of the attacks to grant an absurd bonus that virtually guarantees a hit (like a +5?). Anyway... I've fallen once again into spitballin' and theory-crafting. Sorry.

The short answer to your question is: Yes. But I don't think it's a horrible imbalance. And I think it's mainly only an issue for optimizers. I believe that many, if not most,  players are perfectly happy playing characters that might be suboptimal mechanically, as long as their character feels fun and interesting to play and makes the player feel like they are contributing to the party, story, and game. 

I wasn’t really suggesting that it’s horrible, but I do (personally) favor melee rangers. Also, note the wording change to hunter’s mark it now applies to any attack roll - missile as well as melee (and possibly even magical). Given the slight difference 1HP) between the damage of a longbow and the damages of hand xbows, short swords, and scimitars and HM applying to both ranged and melee attacks I figured looking at hit chances would tell far more than trying to work out ven base damages, but here goes: average damage D8=4.5 HP average base damage D6 = 3.5 HP so: base DPR for a longbow at L1 is .65 x 4.5=2.925. Base damage for a melee is .8775 x 3.5=3.0713 (using my numbers above) - pretty much the same DPR so they are fairly equal. At L2 the longbow jumps up to 0.75 x 4.5 =3.3 HP so the he longbow sis slightly ahead. But the melee fighter has a 2 shots to get 1 hit with a 56% chance of getting both attacks for 7 HP so .56 x 7=3.92 so the melee fighter actually stays ahead. Same thing from L5+ on really the extra attacks do correspond to greater DPR. Another thing to keep in mind is your middle school/HS science classes on the scientific method - everything else needs to be the same when making comparisons in order to actually tell the effects of the 2 you are cmparing - so things like HM actually need to go away not be added in. 

A big issue with TWF on a ranger is uses of bonus action.  So many ranger features are based on Hex being up but if you are fighting groupls of enemies (which in my experience is most combat) you need your bonus action most rounds to change the hex target so can not make an off hand attack.

I think (single weapon) melee and ranged are both viable which is best depends on party composition and the actual combat (e.g. how much space you have, whether you are fighting flying enemies). 

Ranged weapon builds on the new Ranger are not dead, but they do have to be approached differently that in 2014.

A simple example build would be to take a Beastmaster Ranger using the Beast of the Sky as a companion. In combat, you could cast Spike Growth to slow and damage enemies, and then use a Heavy Crossbow, which has the Push mastery, to push enemies through the Spike Growth, causing extra damage and slowing them down even more. All the while, your companion can fly above the enemies and continue to make attacks.

Ranged builds are still entirely viable, they just aren't as dominate as they used to be. I think this is a good thing - being at range has great survivability advantages, so melee damage dealers should have an easier time dealing the most damage since they will also be taking more damage. It's the trade-off of being in the fray vs. sniping enemies from relative safety.

Without going through all the math, you're generally correct. Melee will normally do more damage than Ranged, especially on a build where you get a per-attack bonus like Hunter's Mark.

With that being said, a DPR analysis of a straight Ranger without any sub-class features isn't all that useful beyond the early levels. Indeed, it could be argued that it isn't all that useful even in the early levels.

Of the various Ranger options, only Beastmasters tend to involve a deep investment in the Ranger class.

For non-Beastmasters, you're probably playing some sort of Fighter/Ranger/Rogue mix - and most of that mix is going to be Rogue. So you're going to see a lot more builds that are doing things like using their Bat Familiar to shoot enemies standing in a Sleet Storm from three football fields away.

That is your take on rangers, whis fine - for you. I and a fairly large group on here generally play either pure rangers or ranger dominated multiclasses which tosses much of your argument out. In 2014 there was a sort of consensus that ranged rangers were at least slightly superior to melee rangers - at least n part because of the benefits of the archery fighting style, sharpshooter and sometimes xbow expertise. Those features have changed in 2024 - especially the loss of the -5 to hit with +10 damage if you hit from sharpshooter. In addition, the changes to light weapons and Nick mastery property have changed the balance on the melee side. Yes subclass abilities can somewhat alter the balance but they do so primarily by either adding damage to attacks that hit ( gloomstalker, etc) or by add g additional attacks via outside agents (Beast master). In either case they don’t affect the basic probabilities of hitting which are the root of all damages.

I may be wrong on how I am doing this but I am using a crossbow expert beast master at 5th lvl. bonus action HM in round one. Scimitar/nick 1st attack 1d6 plus HM 1d6, beast strike 2nd attack(charging from 20 feet for 1d8 plus2plus 3Wis bonus plus 1d6) nick moved attack of hand crossbow 1d6 plus HM 1d6. 

Round 2:  Scimitar Nick 1d6, 1d6HM, Hand crossbow 1d6,1d6HM, Hand crossbow 1d6/HM 1d6, bonus action Beast attack

Generally you want to use the bonus action in round 1 first for HM (which you did) then the hand xbow attack first granting advantage from vex on the next attack which would be the second hand xbow attack granting vex advantage again on the final Nick attack. Unfortunately you can’t have the beast attack in round 1 as you only get 1 bonus action and you’ve used it for Hunter’s Mark.  Starting on round 2 you can have the beast attack using your bonus action for a fourth attack.

It really depends on what you are optimizing for.  Ranged builds should take less damage (not in melee, can get cover), and be more capable of maintaining spells (due to less attacks/concentration checks).
Some other damage factors to consider:
1. Ranged builds generally can get attacks off turn 1.  If you can see it, then you can shoot it, while melee martials sometimes require a turn to get into melee.  This might be up to 50% of the time with some DM's.  
2. Ranged builds do better against flying and fleeing targets.  With a longbow  you have the ability to pick off targets unavailable to melee martials.
3. Ranged builds can prioritize high priority non-melee targets.  Wizards need killing.
4. There is more spell support to improve ranged damage (mostly multi target).  Hail of thorns, lightning arrow, etc.

So lets say the ranged character does 20 dpr and the melee character does 30 dpr.  If you combine an extra set of attacks in turn 1 and turn 4 while the melee martial only gets attacks in turns 2 and 3 then the ranged character outdamages the martial 80 points to 60.  You need to evaluate for yourself how these factors play in your game and your play style. 

Personally I prefer melee combatants because I like to really get in the middle of things.  

The thing is that in 2024 a melee ranger that keeps their longbow and arrows can do all of that as well. Ok, not quite as well since they don’t have archery style ( u til a later ASI) but they can do all that. Given the changes to sharpshooter is it really worth prioritizing missile use first over melee any more or should you focus first on melee and add missile  stuff later?