PR Summary

This posts the warnings and deprecations from the doc builds as artifacts, then fetches them from the GitHub Action for CircleCI posting, and posts them as commit checks.

It also removes the URL check that I added in #24579. While it can be fixed, it would still "error" when the build initially starts (because there are no artifacts) and we've lasted without it so far, so I took it out.

Now, I've found out that the status event only triggers for the workflow on the default branch, so the changes here won't be directly reflected until merged (and is why the URL check thing above wasn't noticed before merging). Therefore, I have pushed this change to my fork's main branch, then opened a PR that breaks a reST target and a deprecation in an example. You can see this posting here: https://github.com/QuLogic/matplotlib/pull/25/files

Fixes #22176

PR Checklist

Documentation and Tests

• [n/a] Has pytest style unit tests (and pytest passes)
• Documentation is sphinx and numpydoc compliant (the docs should build without error).
• [n/a] New plotting related features are documented with examples.

Release Notes

• [n/a] New features are marked with a .. versionadded:: directive in the docstring and documented in doc/users/next_whats_new/
• [n/a] API changes are marked with a .. versionchanged:: directive in the docstring and documented in doc/api/next_api_changes/
• [n/a] Release notes conform with instructions in next_whats_new/README.rst or next_api_changes/README.rst