[clang-tools-extra] Clang doc async (PR #93276)

[Paul Kirth via cfe-commits]

https://github.com/ilovepi requested changes to this pull request.

 I've noted several items that need to be addressed in line before this lands. Both the commit title and description need to be updated. Please add a tag `[clang-doc]` to the commit title, and include the full details of the problem you're addressing and how this patch addresses them in the description. 

If this fixes the issue you've referenced, add `Fixes #93273` after the body of the descripton. You can find more info on GitHub interactions w/ commits here https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue

Lastly, this patch badly needs tests. Please create a PR with that demonstrates the existing behavior in a test (or tests) that we can land first. You can rebase this patch on top of it, and we can easily understand the delta between the new and old behaviors based on how the test changed.

https://github.com/llvm/llvm-project/pull/93276