[Meta] GitHub Actions improvements

There are a few minor issues with our GitHub Actions in this repository:

1. The backport workflow uses `secrets.GITHUB_TOKEN`. In consequence, any PR created by the backport action won't run PR checks. This is a documented limitation of the default `GITHUB_TOKEN`. It's not allowed to implicitly trigger any workflow to avoid unwanted loops. In addition, some backports failed due to branch protection rules (e.g. the `workflows` permission was missing for the `GITHUB_TOKEN` which prevents it from being used to modify/add/remove workflow files).

2. In some of our workflows we are using `secrets.PAT`. This one belongs to a regular user (me) and not to a technical one (e.g. elasticmachine). This makes it hard to check if a workflow was triggered by an automation or an actual user (`github.actor == 'elasticmachine'`) as we can never be sure the action was not really triggered by the user if we compare the actor to his username.

Start by locating the backport workflow and the other workflow files that reference secrets.PAT. Review how their token permissions, pull-request checks, and actor detection currently behave. Done means the documented backport and automation-identification problems are addressed without weakening workflow protections.

Written by the indexing model from the issue text.