CI: Using docstring validator from numpydoc
- [X] xref #28822
- [x] tests added / passed
- [X] passes `black pandas`
- [X] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry

We moved our script to numpydoc, and it already had some improvements there. The script does like 80% of our validation, so what I'm doing here is to call numpydoc validation, and then call our custom validation (things that for different reasons weren't moved to numpydoc).