BUG: [ArrowStringArray] Recognize ArrowStringArray in infer_dtype
PR is draft. follow-up to #40679, https://github.com/pandas-dev/pandas/pull/40679#issuecomment-809642594 which is not yet merged and need to make window to run benchmarks https://github.com/pandas-dev/pandas/pull/40679#pullrequestreview-623553887

on master

```
>>> pd.__version__
'1.3.0.dev0+1180.gdd697e1cca'
>>> 
>>> from pandas.core.arrays.string_arrow import ArrowStringDtype
>>> 
>>> arr = ArrowStringDtype.construct_array_type()._from_sequence(["B", pd.NA, "A"])
>>> 
>>> arr
<ArrowStringArray>
['B', <NA>, 'A']
Length: 3, dtype: arrow_string
>>> 
>>> pd._libs.lib.infer_dtype(arr)
'unknown-array'
>>> 
```