ENH: [ArrowStringArray] Enable the string methods for the arrow-backed StringArray
from https://github.com/pandas-dev/pandas/issues/35169#issuecomment-712883859

> Enable the string methods for the arrow-backed StringArray. This might also need some additional changes in the string accessor code (eg to dispatch extract to the underlying array as well)


@simonjayhawkins is this still draft? (it seems ready to me) this one goes in after #40725, https://github.com/pandas-dev/pandas/pull/40708#discussion_r605101764, over 80% complete on the benchmarks. To be able to move forward with the different PRs, I think it is perfectly fine to merge this with the ` "arrow_string": "string",` in infer_dtype (which *is* the name of the dtype on current master), and then this can be updated when the name gets changed or in #40725 @simonjayhawkins this is ready for review/merge now? hopefully, will mark as ready for review once ci is green. @jorisvandenbossche green @jorisvandenbossche green. ok to merge? Yep, thanks!