[Feature Request] Replace delete backport branch workflow with native GitHub functionality

[dbwiddis]

Is your feature request related to a problem? Please describe

Backports are handled by a GitHub Action workflow which is executed by a bot with more power than the PR approver, and requires special measures to carefully only delete just the right things.

GitHub has a native feature that does the same thing, without requiring a super-power bot. It only deletes things that the issue approver has permissions for.

Describe the solution you'd like

Enable the GitHub feature to do these branch deletions automatically. (Repo owners can always restore them if they want!)

Then delete the workflow.

I've done this on repos I maintain. It should be done here as well, but requires admins to configure it since the wonderful GitHub permissions allow maintainers to enable dangerous auto-merging but not harmless auto-deleting-with-recovery.

Related component

Other

Describe alternatives you've considered

Status quo.

Additional context

This should probably be implemented organization wide, along with many other GitHub niceties, but let's keep the scope of this to this one feature for now.