DEPR: Deprecate core
- [x] closes #27522 
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

I haven't actually performed the refactor(pandas.core -> pandas._core) yet so tests are failing because of the warnings. 

I think I'd prefer doing this as a DeprecationWarning before elevating to a FutureWarning.

That will give downstream libraries a chance to report the pieces of functionality they need from `pandas.core` a chance to report and fix the warnings before their users see it.