CI: Update weekly dependency test job - #22785

PR Summary

The weekly dependency test was creating multiple issues when several
of the matrix jobs would fail. To fix that, we move the issue creation
script to a new job to only be triggered once. Additionally, add in the
job run link for quicker reference to the CI failure.

I did a quick test of this on my fork and it appears to be working as I'd expect.
Success (didn't run the upload issue): https://github.com/greglucas/matplotlib/actions/runs/2096657469
Failure (did run the upload issue with the correct run link in the logs): https://github.com/greglucas/matplotlib/actions/runs/2096667795

PR Checklist

Tests and Styling

• [N/A] Has pytest style unit tests (and pytest passes).
• [N/A] Is Flake 8 compliant (install flake8-docstrings and run flake8 --docstring-convention=all).

Documentation

• [N/A] New features are documented, with examples if plot related.
• [N/A] New features have an entry in doc/users/next_whats_new/ (follow instructions in README.rst there).
• [N/A] API changes documented in doc/api/next_api_changes/ (follow instructions in README.rst there).
• [N/A] Documentation is sphinx and numpydoc compliant (the docs should build without error).