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

[cvm-a]

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

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

INSTALLED VERSIONS

commit : d9cdd2e
python : 3.11.6.final.0
python-bits : 64
OS : Darwin
OS-release : 23.5.0
Version : Darwin Kernel Version 23.5.0: Wed May 1 20:14:38 PDT 2024; root:xnu-10063.121.3~5/RELEASE_ARM64_T6020
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.2
numpy : 1.24.4
pytz : 2024.1
dateutil : 2.9.0.post0
setuptools : 70.0.0
pip : 23.2.1
Cython : 3.0.10
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : 3.2.0
lxml.etree : 5.2.2
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.4
IPython : 8.24.0
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.3
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2024.5.0
gcsfs : 2024.5.0
matplotlib : 3.9.0
numba : 0.57.1
numexpr : None
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 16.1.0
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.13.1
sqlalchemy : None
tables : None
tabulate : 0.9.0
xarray : None
xlrd : 2.0.1
zstandard : None
tzdata : 2024.1
qtpy : None
pyqt5 : None

[mroeschke]

Thanks for the report. Currently groupby ops in pandas are all numpy based, so arrow types are converted to numpy first using _to_masked. Looks like there currently no conversion in that method to "numpy strings".

[chaarvii]

take