TST: Add any_string_dtype parameterization to test
- [x] tests added / passed
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit) for how to run them

xref https://github.com/pandas-dev/pandas/pull/44876#discussion_r770374539
Thanks @mroeschke 