GitHub Actions: Add Python 3.14 to test matrix with deps

[cclauss]

Summary

Checklist

Combines #3645 + #3653 + #3654 but still pytests do not start on Python 3.14rc2.

• GitHub Actions: Add Python 3.14 to test matrix #3645 and
• Bump the python-packages group across 1 directory with 11 updates #3653 and
• Upgrade Python type checker mypy #3654

• I understand that this PR may be closed in case there was no previous discussion. (This doesn't apply to typos!)
• I've added a test for each change that was introduced, and I tried as much as possible to make a single atomic change.
• I've updated the documentation accordingly.