Unwind _inner call pattern in api object modules

[tychedelia]

Removes the _inner system pattern and moves a bit more coordination back into lib.rs.

Originally, this pattern arose organically because it was annoying to work with explicit borrows over World. Bevy provides the In parameter for systems which can be used when explicitly executing a system on World. This cleaned code up, but when refactoring things to live in modules, I had wanted to keep lib.rs as small as possible.

However, this pattern is kind of ugly. There are a few cases where, particularly because of code re-use, we need to do a little bit more coordination, but for the most part we typically can just call the the system immediately, and it's cleaner to have lib.rs do this.

This change should be basically mechanical and introduce no behavior changes. Please see the docs folder for some additional color here.