Add CI checks to ensure quasi-duplicate APIs stay synchronized

With #9686 merged too, I wonder if there's a way we could automatically check or enforce that all of the methods and docs are kept in sync 🤔 A trait won't work, both because of ergonomics / discoverability, and because `QueryState` needs a `World`. We could use some horrible macro, but that hurts code readability. Maybe a CI check? I guess that's a question for another PR though.

_Originally posted by @alice-i-cecile in https://github.com/bevyengine/bevy/issues/9774#issuecomment-1714881928_

Start by reviewing issue #9774 and the changes in #9686 to identify the quasi-duplicate APIs and their associated documentation. Define a CI check that detects when the methods or docs diverge; done means the check reliably reports synchronization failures without requiring a macro.

Written by the indexing model from the issue text.