Making other models move relative to an animation?

I have a Mech that’s meant to use interchangeable parts; swap out torso, arms, legs, etc.

I would prefer to keep the models separate to make that as easy as possible, but when the legs are animated, nothing else moves with them. Arms also have their own animations depending on what’s happening as well as the ‘head’ of it.

Gif of legs moving without upper body:

Image of all the models grouped under one ‘super’ model.

Any thoughts on if there’s an easy way to fix this?