(feat): Support for pandas ExtensionArray

[ilan-gold]

Some outstanding points/decisions brought up by this PR:

• Confirm type promotion rules and write them out. As it stands now, if everything is of the same extension array type, it is passed onwards and otherwise is converted to numpy. (related: Avoid coercing to numpy in as_shared_dtypes #8714)
  - [ ] Acceptance of plum as a dispatch method. Without it, the behavior should be fallen back on from before (cast to numpy types). I am a big fan of dispatching and think it could serve as a model going forward for making support of other data types/arrays more feasible. The other option, I think, would be to just use the underlying array of the ExtensionDuckArray class to decide and then have some central registry that serves as the basis for a decorator (like the api for accessors via _CachedAccessor). That being said, the current defaults are quite good so this is a marginal feature, in all likelihood.
• Do we allow just pandas ExtensionArray directly or can we also allow Series?

Possible missing something else! Let me know!

Checklist:

• Closes Categorical Array #8463 and Closes Support for pandas Extension Arrays #5287
• Tests added
• User visible changes (including notable bug fixes) are documented in whats-new.rst
• New functions/methods are listed in api.rst

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[TomNicholas]

This looks like a big feature addition!

I'm very ignorant of ExtensionArrays - but is it possible to imagine a design where ExtensionDuckArray conforms well enough to the duck array structure that xarray expects that ExtensionDuckArray could live entirely outside of xarray? I'm also curious why we need isinstance(data, ExtensionDuckArray rather than calling our already-existing is_duck_array(data).

[ilan-gold]

What's the status here?

[dcherian]

Sorry, this fell off my radar. Can you open an issue regarding the to_dataframe problem?

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