what kind of tools are needed for making these animations

They are motion-captured and/or they're animated by hand in your 3D editor, e.g. Blender

But much more likely is you won't be making animations, you'll be buying them (or getting them for free). There are many places you can buy these animations already, already rigged to a skeleton.

Some examples (I don't endorse them specifically):

https://characters3d.com/

https://www.unrealengine.com/en-US/blog/game-animation-sampl...

    skeletal animation. how are you supposed to think about this

Think about giving direction to an actor. You give high-level instructions to the animation system, and it picks the animation based on rules about what animation to use in what situation, that you already set up. It manages the transition to the next animation, all of which are animations of the skeleton, that the character model adapts to (including physics-based parts of the character like hair and cloth)

Generally speaking, you define animation cycles (e.g. walk cycle, run cycle), and then transition between two different animations that are in phase with each other, but it can be a lot more complicated in order to look more natural.

Unity has the Animation Controller. Unreal has "Motion Matching". Godot has Animation Trees.

     do we need intermediate animations

If you want to, yes, but also you can have the game engine interpolate

You haven't even mentioned things like having the character's feet stand realisticly on non-level ground. For that you would use inverse kinematics, but not too much of it because it has a tendancy to go wonky

    are there LLM tools

Yes but you'd be better off with animations someone has already created, they tend to look better. Many companies now offering AI-based 3D character generators too.

    formats like obj, fbx, m3d, glb etc. the same data stored in these files in a slightly different way

They all have different purposes. You want glTF/glB (same format but in text vs binary) for most purposes

Try out this FPS game project for the Godot Engine: https://github.com/godotengine/tps-demo