API: Replace na_action parameter in Series/DataFrame/Index.map by the standard skipna
- [X] xref #61128
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We've been consistently using a boolean `skipna` parameter to let users decide whether missing values should be ignored or not in different methods. The `.map` method has an awkward `na_action=None | "igonre"` for the same purpose. I add the standard `skipna` parameter to the methods, and start the deprecation of the `na_action` one.
Updated this so the `na_action` parameter is also not removed from the extension arrays, and it warns. The base array since as you said @mroeschke is technically public. `map_array` since it's used by pandas-pint, even if it's not supposed to be public, but better not break their code. And the specific implementations that subclass the base extension array to keep the same signature. mypy complained, and also better to keep the signatures the same even if it's a temporary thing.

I think this should be ready to merge now. This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this.