[ci] Split formatting and docs checks into separate task (backport #2749)

[mergify]

This is an automatic backport of pull request #2749 done by Mergify.
Cherry-pick of ed26942 has failed:

On branch mergify/bp/3.5.x/pr-2749
Your branch is up to date with 'origin/3.5.x'.

You are currently cherry-picking commit ed269429.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   .github/workflows/test.yml

no changes added to commit (use "git add" and/or "git commit -a")

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/github/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

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