This seems like a great starting point. If I were to add this to my game, I'd feel confident adding everything else I need from here. I agree that the jump at runtime stuff is a good idea. That makes other modular kinds of movement really easy to plug in when necessary.
As far as "what should be included in core", I think anything related to movement is a good idea. Sprinting, jumping, crouching, interacting, state machine maybe? (can't tell if that's already in there) is everything I think of as "core" to an FPS controller. Everything else like shooting, flashlight, headbob, climbing are a bit more niche to certain genres. I do think that there's probably a person out there that would want everything out the box, so I think it would be prudent to add an "everything" pack similar to how the kenney asset store does it.
All in all, a pretty satisfying start! Well done!