This workflow runs the PR and Push workflow files on a `pull_request`
trigger. The intent is to test changes to the workflow files
immediately. Previously, these were run directly from the respective
workflow files.

The new approach allows us to move the logic to run this only when
workflow files changed from the pull_request trigger into a job. This
has the advantage that older jobs are cleaned up, when the PR changes
from a state of "workflow files changed" to "no workflow files changed".
This can happen when changing a PR's base from staging to master, in
which case changes from master would temporarily appear in the PR as
changes. When these include changes to workflow files, this would
trigger the PR workflow via `pull_request`. Once the base is changed,
the PR is closed and re-opened, so CI runs again - but since it's on the
same commit and the new run doesn't trigger `pull_request`, the results
of the previous run are still kept and displayed. These results may
include cancelled or failed jobs, which are impossible to recover from
without another force-push.

Checking this condition at run-time is only possible, because we move it
into a separate workflow, turning the `pr.yml` workflow into a re-usable
workflow. This will make sure to skip the whole workflow at once, when
no change was detected, which will prevent the "no PR failures" job from
appearing as skipped - which would imply "success" and make the PR
mergeable immediately. Instead the "no PR failures" job is not shown at
all for this trigger, which is generally what we want.

Do the same for `push.yml` for consistency.

(cherry picked from commit 443f30f)

Previously, the test for the push workflow was running on the HEAD
commit of the PR only. It would be better to run it on the merged result
instead, just like any other tests we run in a PR.

(cherry picked from commit 06a0eba)

Changes to the merge-group workflow should also validate that the file
is hooked up correctly and works - otherwise we risk merging CI changes
that cause the merge queue to fail consistently.

(cherry picked from commit 534d41e)