ci: Remove `paths-ignore` for docs, as it does not work with required status checks (#23424)

This PR removes the `paths-ignore` for docs again, as it causes
docs-only PRs to be unmergable in combination with required status
checks (which we need in order to support merge-when-ready).

We can put these back if and only if we come up with a solution for how
to make it work with required status checks.

Release Notes:

- N/A