API: improve dtype in df.where with EA other
- [ ] closes #xxxx (Replace xxxx with the GitHub issue number)
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Improves the patch-job done by #38742.  Also makes the affected test robust to always-distinguish NAN-vs-NA behavior.
Looks like [`87d5fdf`](https://github.com/pandas-dev/pandas/pull/62038/commits/87d5fdfd1983c6408033f22009bab7b5b0d1be07) undid all your changes before Woops.  Looks better now. ```
ruff format.............................................................................................Failed
- hook id: ruff-format
- files were modified by this hook
```

Any idea how to make it tell me what it wants to change? You can comment `pre-commit.ci autofix` in this PR to get pre-commit to add a commit to fix it for you.

Otherwise if you have the pre-commit hooks installed, to show the fixes you'll probably need to add `--show-fixes` on this line 

https://github.com/pandas-dev/pandas/blob/84757581420cfcc79448aa3274e28d90aaf75c87/.pre-commit-config.yaml#L25 running `ruff format` locally on the affected files says it leaves them unchanged What about running `pre-commit run ruff --all-files`? (Generally `pre-commit run <id to check>` is the source of truth for the linting checks) That did it, thanks.  Lets see if the CI agrees Booyah, did it. Thanks for help troubleshooting Np! Thanks @jbrockmendel 