CI: Implement clangd-tidy as GitHub Action

[Repiteo]

Replaces our current clang-tidy checker in CI with a clangd-tidy equivalent. This integrates the more lightweight checker in a way that's directly integrated with our repository & should have a wider coverage than the clang-tidy pre-commit hook

Example output on filtered files can be viewed on this runner from a dummy commit.

[akien-mga]

Does it currently pass if running manually on all files (except the ones excluded by the changed-files logic)?

Also, running it on all files is pretty slow (more than one hour on my laptop) so it may timeout on CI. This may turn out to be problematic on big codebase wide changes. If so we might want to put a threshold on how many files the changed-files action returns, and bail out if it's too high.

[Repiteo]

The workflow now passes when run across all filtered files! What's more: the time it would take to run against every passable file is ~45 minutes¹, so undeniably a step up from the speed of clang-tidy despire having to process many more files. I can't imagine a scenario where we'd be adjusting that many files in the first place, so I think it'd be safe to keep the integration as-is

Footnotes

1. https://github.com/godotengine/godot/actions/runs/23328268617/job/67854140563 ↩

[akien-mga]

Thanks! Great work 🎉