String dtype: honor mode.string_storage option (and change default to None)

[jorisvandenbossche]

At the moment, the pd.options.mode.string_storage option defaults to "python", and the StringDtype() constructor just ignores it when constructing the future default NaN-variant (i.e. the option is only used for creating the NA-variant), but uses the logic of "use "pyarrow" if installed otherwise "python"".

Given this option exists, I think it makes sense to let it always be honored, so that a user can actually control this through the option (and also for testing this makes things a bit easier to check the behaviour in case pyarrow is not installed without uninstalling/installing it constantly).

In order to honor the option, I changed the default to None to mean this "use "pyarrow" if installed otherwise "python"" logic as default if constructing the NaN-variant.
When constructing the NA-variant, for now None still gets translated to "python". I think we should also change the default for this dtype to use pyarrow if installed, but that's a change only for 3.0, I think (not to backport for 2.3), so therefore didn't include that in this PR.

xref #54792

[jorisvandenbossche]

Should I use "auto" instead of None for the default? (for some other options like the parquet engine we use "auto" for the default that depends on what is installed)

[WillAyd]

Should I use "auto" instead of None for the default? (for some other options like the parquet engine we use "auto" for the default that depends on what is installed)

Yea I prefer auto for string options like this

[WillAyd]

lgtm ex changing None to auto

[mroeschke]

Thanks @jorisvandenbossche