REGR: groupby.count on string[pyarrow] returns column with string dtype instead of integer

[phofl]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

pdf = pd.DataFrame({"a": [1, 2, 3], "b": pd.Series(["a", "b", "a"], dtype="string[pyarrow]")})
pdf.groupby("a").count().dtypes

Issue Description

b    string[pyarrow]
dtype: object

this is a regression on main

Expected Behavior

b    int64
dtype: object

Installed Versions

Replace this line with the output of pd.show_versions()