BUG: idxmax and idxmin raising for all na ea series
- [x] closes #51276 (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).
- [x] 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.

Not sure if NA or NaN makes more sense. I think we have a couple of ops where we return nan even for ea dtypes when the result is a scalar
xref #33941 why closing?  i was looking forward to getting #33941 resolved (i think it has implications for fixing some of our groupby xfails) Did not look like there was consensus and we had tests covering the changed behavior. But can revisit if you think we should change it Let's try to discuss the desired behavior here on the next dev call?  I think this is an area where we need to Just Make A Decision.