Use GitHub App rather than the workflow GITHUB_TOKEN to commit `make docs` procedure updates

[jdbaldry]

The latter token doesn't trigger CI by design to prevent recursive workflow invocations.

If we use a GitHub App to commit the changes, there will be no need for empty "Trigger CI" type commits.

This is especially valuable in repositories like grafana/pyroscope where Grafana Labs employees can only contribute via forks.

[jdbaldry]

For example, grafana/pyroscope#3802

[robbymilo]

Is this still a problem?

[jdbaldry]

Think so yeah. Could also consider a job that we run from Writers' Toolkit to push the updates so we don't have to propagate a secret to all the repositories.