2014 rules were pretty clear on the fact that claws and teeth were "natural weapons". The 2024 PHB doesn't mention natural weapons, but instead defines weapons explicitly as "objects". Does anyone know if a 2024 Druid can still use Savage Attacker in beast form, or does the feat now only apply to hand held objects? 

The Rules Glossary defines "Weapon" as "an object that is in the Simple or Martial weapon category" and none of the stat blocks in the Player's Handbook use the term "weapon attack", opting for "Melee Attack Roll" or "Ranged Attack Roll" instead. Seems pretty open and shut that Savage Attacker only works with objects. The 2014 version arguably didn't either since it mentioned "the weapon's damage roll", but it's a lot more explicit about it now.

Now that you mention it, Alter Self was also reworded to remove mention of natural weapons.

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For now, the term "Natural Weapon" isn't defined.

IIRC, the term "natural weapons" first appears in the 2014 Monster Manual (p. 10):

The most common actions that a monster will take in combat are melee and ranged attacks. These can be spell attacks or weapon attacks, where the "weapon" might be a manufactured item or a natural weapon, such as a claw or tail spike.

Now, 2024 rules. A reference to monsters' attacks can now be found in the Melee Attacks paragraph (emphasis mine):

A melee attack allows you to attack a target within your reach. A melee attack typically uses a handheld weapon or an Unarmed Strike. Many monsters make melee attacks with claws, teeth, or other body parts. A few spells also involve melee attacks.

And if an Unarmed Strike is defined as follows (emphasis mine):

Instead of using a weapon to make a melee attack, you can use a punch, kick, head-butt, or similar forceful blow. In game terms, this is an Unarmed Strike—a melee attack that involves you using your body to damage [...]

Does this mean that monster attacks made with their "body parts" (*) now count as Unarmed Strikes?

(*) previously known as natural weapons.

We had this answer in the Sage Advice Compendium. It'd be nice to have a new SAC updated with the 2024 rules.

Are natural weapons considered weapons?
Things designated as weapons by the rules, including natural weapons, are indeed weapons. In contrast, unarmed strikes are not weapons. They are something you do with an unarmed part of your body.

I'm leaning towards yes. They're definitely excluded from the definition of weapons, they do fit the definition of an Unarmed Strike, and the rules changed a whole lot of other things to better align with player expectations (e.g. grapples and Psychic Blade attacks as opportunity attacks, bonus action potions, dual wielding hand crossbows, area effects dealing damage immediately instead of on the enemy's turn, and the Bonus Action spell rule being simplified to how everyone misquoted it.) Unarmed Strikes came up over and over again when discussing Wild Shape and every time a species with a natural weapon got added they kept having to specify "and you can make unarmed strikes with it."

The one thing that casts a bit of doubt is the text from the Melee Attack rules section you quoted; they seem to be juxtaposing 3 different things (the normal case, monsters, and spells) and the bit about many monsters using claws, etc. is a bit redundant if they fall under Unarmed Strikes now. That's not super strong evidence, and I'd still bet money on natural weapons being unarmed strikes now, but until the Monster Manual comes out I'd take that with a grain of salt.

I’d be hesitant to assume that “natural weapons” count as Unarmed Strikes now. For PC species in MotM, those that give “natural weapon”-like features (e.g: centaur hooves, Tabaxi claws) are defined as modifications to your Unarmed Strikes: a higher damage dice and sometimes a change of damage type. The beast stat blocks in the new PHB make no reference to Unarmed Strikes: they are essentially unique actions that the beast can take which involve making a melee attack. 

Hopefully, whether they count as Unarmed Strikes will be clarified, though there might then need to be clarification whether, e.g. a Monk/Druid wildshaping into a Giant Badger would swap the damage dice from 2d4 to 1d6 or to 2d6.

Agreed, beast attacks seem to be a wholly separate (though ill-defined) type of thing. Apart from the question of damage dice, the rules as written also state that "Whenever you use your Unarmed Strike" you have an option to grapple a target. Hard to imagine being grappled by a horse or a camel. It's strange how ill-defined this is, given all the obvious thought and effort applied to revamping moon Druids.

Quote from InquisitiveCoder >>

I'm leaning towards yes. They're definitely excluded from the definition of weapons, they do fit the definition of an Unarmed Strike, and the rules changed a whole lot of other things to better align with player expectations (e.g. grapples and Psychic Blade attacks as opportunity attacks, bonus action potions, dual wielding hand crossbows, area effects dealing damage immediately instead of on the enemy's turn, and the Bonus Action spell rule being simplified to how everyone misquoted it.) Unarmed Strikes came up over and over again when discussing Wild Shape and every time a species with a natural weapon got added they kept having to specify "and you can make unarmed strikes with it."

The one thing that casts a bit of doubt is the text from the Melee Attack rules section you quoted; they seem to be juxtaposing 3 different things (the normal case, monsters, and spells) and the bit about many monsters using claws, etc. is a bit redundant if they fall under Unarmed Strikes now. That's not super strong evidence, and I'd still bet money on natural weapons being unarmed strikes now, but until the Monster Manual comes out I'd take that with a grain of salt.

 I've the same feeling and I also share the same doubts.

In 2014, we learned how Wild Shape interacts with Unarmed Strikes, thanks to answers in the SAC/Twitter or useful threads like this one: Wild Shape question. If this interaction is allowed now, it's something we'll need to re-learn.

As a side note, I just realized that I wrote a few weeks ago about Druids and Monks in 2024 Wild Shape - Do You Gain Multiattack?

I will write again there to reference this thread with these new details and discussions. I don’t want to confuse anyone.

Quote from ThelenyiWhinlaw>>

For PC species in MotM, those that give “natural weapon”-like features (e.g: centaur hooves, Tabaxi claws) are defined as modifications to your Unarmed Strikes: a higher damage dice and sometimes a change of damage type.

That's been a thing as far back as Volo's Guide to Monsters in 2016. That's part of why I'm saying it makes sense to just make natural weapons unarmed strikes by default. It changes absolutely nothing about how monsters are run because monsters almost never have any features that'd interact with US. But it streamlines a lot of things on the player side, and you no longer have this weird category of things that isn't quite an unarmed strike, but also not quite an attack with a weapon, and that very few game rules actually interacted with (there's no feats, class features, spells or monster traits that enhance or protect against natural weapons.)

The beast stat blocks in the new PHB make no reference to Unarmed Strikes: they are essentially unique actions that the beast can take which involve making a melee attack.

The new stat blocks don't tell you if something is a weapon attack either, even in cases where they clearly involve a handheld weapon (e.g. the Skeleton.) That information is normally not relevant to running a monster, and it'd be even less relevant if natural weapons count as unarmed strikes as a general rule.

Quote from Clovstool>>

Apart from the question of damage dice, the rules as written also state that "Whenever you use your Unarmed Strike" you have an option to grapple a target.

They'd use the same damage dice as players if they opt to use the generic damage option for some reason. This was possible under the 2014 rules as well, because monsters can use any of the universal actions in the Player's Handbook in addition to the ones in their stat block.

Hard to imagine being grappled by a horse or a camel. It's strange how ill-defined this is, given all the obvious thought and effort applied to revamping moon Druids.

They can bite. And the Grappling entry in the Rules Glossary now accounts for non-human anatomy, whereas the 2014 version only mentioned hands. That led to a lot of confusion since the Monster Manual said monsters could use the universal actions listed in the PHB as well, but the 2014 PHB was written for player characters. It then had to be clarified in Sage Advice.

Is the grappling rule in the Player’s Handbook usable by a handless creature?

The grappling rule was written for a grappler with at least one hand, but a DM can easily adapt the rule for a handless creature that has a bite or an appendage, such as a tentacle, that could reasonably seize someone. A wolf, for example, could plausibly try to seize a person with its bite, and the animal wouldn’t be able to use its bite attack as long as it held onto the person.

Keep in mind that the grappling rule in the Player’s Handbook requires the Attack action, so a creature must take that action—rather than Multiattack or another action in the creature’s stat block—when it uses that rule. A monster, such as a roper, that has a special grappling attack doesn’t follow that rule when using its special attack

EDIT: I had linked to the wrong Sage Advice question.

Just noticed something else that's relevant. Enlarge/Reduce was updated to say it subtracts 1d4 damage when a reduced target attacks with shrunken weapons or Unarmed Strikes. This addressed a gap in the old version where only attacking with reduced weapons was affected. Seems unlikely they would intend for claws, etc. to be a third category but forget to include them here.

Quote from ThelenyiWhinlaw >>

I’d be hesitant to assume that “natural weapons” count as Unarmed Strikes now. For PC species in MotM, those that give “natural weapon”-like features (e.g: centaur hooves, Tabaxi claws) are defined as modifications to your Unarmed Strikes: a higher damage dice and sometimes a change of damage type. The beast stat blocks in the new PHB make no reference to Unarmed Strikes: they are essentially unique actions that the beast can take which involve making a melee attack. 

Hopefully, whether they count as Unarmed Strikes will be clarified, though there might then need to be clarification whether, e.g. a Monk/Druid wildshaping into a Giant Badger would swap the damage dice from 2d4 to 1d6 or to 2d6.

 If that's the case, then because of how Attack of Opportunity is worded "To make the Opportunity Attack, take a Reaction to make one melee attack with a weapon or an Unarmed Strike against the provoking creature", monsters can't make opportunity attacks. Unless, of course, they had a physical weapon in their hand or just wanted to unarmed attack you. That doesn't make much sense. 

I believe monsters attack using Action their statblocks or Unarmed Strike. Natural Weapon otherwise appear in Alter Self with the following text:

Natural Weapons. You grow claws (Slashing), fangs (Piercing), horns (Piercing), or hooves (Bludgeoning). When you use your Unarmed Strike to deal damage with that new growth, it deals 1d6 damage of the type in parentheses instead of dealing the normal damage for your Unarmed Strike, and you use your spellcasting ability modifier for the attack and damage rolls rather than using Strength.