Have a dashboard that reports the modules with failing remote tests

I'm just brainstorming about the ways that will help us noticing, assigning, and addressing failing remote tests in a timely manner. One way would be a dashboard, or another a github action that also pings those who are maintaining the given module: https://github.com/astropy/astroquery/pull/1446 (if there is someone at archives, the rest of the modules would remain in the "best effort" category by the library maintainers).

E.g. the list in #2203 will become outdated very soon.

Start by reviewing the failing-test list in #2203 and the maintainer-notification example in pull request #1446. Define whether the outcome is a dashboard or GitHub Action, and consider the work complete when it reports current failing remote tests by module and identifies the relevant maintainers or best-effort ownership.

Written by the indexing model from the issue text.