[7.17] ci(release): automate release steps for the patch (backport #12273)

[mergify]

This is an automatic backport of pull request #12273 done by Mergify.
Cherry-pick of 1b36392 has failed:

On branch mergify/bp/7.17/pr-12273
Your branch is up to date with 'origin/7.17'.

You are currently cherry-picking commit 1b3639226.
  (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/rm <file>..." as appropriate to mark resolution)
	both modified:   .github/workflows/run-patch-release.yml
	deleted by us:   release.mk

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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[v1v]

Requires #12366

[mergify]

This pull request has not been merged yet. Could you please review and merge it @v1v? 🙏

[v1v]

This PR also contains the changes from #12366

[v1v]

I reverted 9c06696 so I can verify if the lint works nicely rather than failing dramatically.

And it did work as expected -> https://github.com/elastic/apm-server/actions/runs/7559406648/job/20583139806?pr=12397

[v1v]

run elasticsearch-ci/docs

[v1v]

I'll create a specific PR with the reverted changes in #12397 (comment)