Pandas BUG: groupby.rank is not supported for large_string[pyarrow] dtype

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Reproducible Example

import pandas as pd
import pyarrow as pa

df = pd.DataFrame(
  {
    "a": list(range(10)) * 2,
    "b":list(range(20,30)) * 2,
    "c":list(range(50,70)),
  },
 dtype=pd.ArrowDtype(pa.string())
)

result = df2.groupby(["a", "b"], as_index=False)["c"].rank(method="first", ascending=False, na_option="bottom")

Issue Description

This is similar to #51996. When grouping a dataframe and applying the rank function on a column with data type string[pyarrow] or large_string[pyarrow] I get the following error: TypeError: rank is not supported for string[pyarrow] dtype or TypeError: rank is not supported for large_string[pyarrow] dtype respectively

Expected Behavior

I would expect rank to work for string[pyarrow] just as it works for the pandas "string" dtype, using lexicographic ordering.

Installed Versions