REGR: prefer user-provided mode
follow-up to #39253

- [x] closes #39247
- [x] tests added / passed
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [x] whatsnew entry

Make sure that the user-provided mode is always preferred (if it contains 't' or 'b') and extend list of text-only classes.