Verify on CI that localhost featuregate changes are copied across repositories

[mx-psi]

          I'm wondering if there's a good way to enforce keeping this up to date `core`. There will be times they differ, but it should only be temporarily. There should be a PR opened for both repositories, one will just get merged before the other.

It could be a CI check that simply fails whenever a user changes the contents of these files, warning the user that core needs updated as well. A triager, approver, or maintainer could then come, confirm a PR is also opened against core, and then add some kind of skip label that ignores the check? Or just approve and merge it with the failing CI action knowing it's not an issue. If it's a CI action it would also need to be in core to make sure contrib stays up to date as well.

Otherwise we could add a CI action that simply compared file contents and fails when they don't match. This would be a bit more involved and would fail in unrelated PRs, which would be confusing.

I don't want to make it too complicated but speaking from experience, a comment at the top of a file is pretty easy to miss.

Originally posted by @crobert-1 in #30774 (comment)

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