Invite organization members based on merged PRs: Not working out so well (currentled DISABLED)

https://github.com/astropy/astropy-tools/actions/workflows/update_org_members.yml

It silently stopped working last month. I don't want another cron job to babysit. We need to figure out how to have it run unsupervised and actively tell us when something isn't right. And when it does run successfully, a status report on who was invited would be nice.

I don't think GitHub Actions is the right home for this because:

* GitHub stops it if we stop modifying it.
* We cannot control who GitHub notifies. Whoever last touched the file is the person notified. If this person does not check notification or does not care, things fall through the crack.

Start by reading .github/workflows/update_org_members.yml and reviewing its recent workflow history. Clarify how the existing merged-PR invitation process should run without supervision and how failures should notify maintainers. Done means reliable unattended execution, actionable failure notification, and a successful-run report listing invited members.

Written by the indexing model from the issue text.