ENH: Enable fillna(value=None)
- [x] closes #57723 (Replace xxxx with the GitHub issue number)
- [ ] [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
- [ ] 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.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

The one behavior introduced here I think is important to highlight is using `None` with non-object dtypes. In such a case we treat `None` as the NA value for the given dtype for NumPy float/datetime and pandas' EA dtypes. However for external EAs, by default we try to put `None` in the values and raise if this fails.

For object dtype, we replace any NA value with `None`.

cc @Dr-Irv 
Thanks @rhshadrach 