ci: Run required status checks for docs-only PRs, but exit early (#22254)

I noticed a problem with the addition of required status checks where
PRs that only touched the docs wouldn't pass the status checks due to
all of the checks being skipped via `paths-ignore`:

<img width="950" alt="Screenshot 2024-12-19 at 11 16 38 AM"
src="https://github.com/user-attachments/assets/a6fa43ee-de63-40a6-a15a-f2f3519e9db8"
/>

This PR aims to address this by making it so required status checks run
for docs-only PRs, but exit early (before doing all of the work).

Release Notes:

- N/A