ENH: Allow ArrowDtype(pa.string()) to be compatable with str methods

[mroeschke]

This implementation is somewhat similar but kept separate to the methods in ArrowStringArray because I tailored ArrowExtensionArray to always return ArrowExtensionArray (most obvious in _str_map) as opposed to falling back to pandas masked arrays.

Additionally:

• any_string_method pytest fixture to pandas/conftest.py so it can be used by extensions/test_arrow.py
• Removed some imports into pandas/core/strings/__init__.py as it was causing a circular dependency when adding this to ArrowExtensionArray

[mroeschke]

Closing in favor of #51207