CLN: Remove StringMixin from PandasObject
- [x] closes #26495
- [ ] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

Addresses #26495. In addition to the use of StringMixin in PandasObject, StringMixin is also used in core.computation and the io.pytables. I'd like to tackle those in a different PR, as there is some funkyness there (calls that depend on frame depth etc.)
