BUG: zfill with pyarrow string

[williambdean]

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

pd.Series(["A", "AB", "ABC"], dtype=pd.ArrowDtype(pa.string())).str.zfill(3)

Issue Description

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/will/GitHub/various/narwhals/.venv/lib/python3.12/site-packages/pandas/core/strings/accessor.py", line 137, in wrapper
    return func(self, *args, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/will/GitHub/various/narwhals/.venv/lib/python3.12/site-packages/pandas/core/strings/accessor.py", line 1818, in zfill
    result = self._data.array._str_map(f)
             ^^^^^^^^^^^^^^^^^^^^^^^^^
AttributeError: 'ArrowExtensionArray' object has no attribute '_str_map'. Did you mean: '_str_pad'?

Expected Behavior

Same as other string dtypes

Installed Versions

INSTALLED VERSIONS

commit : 0691c5c
python : 3.12.9
python-bits : 64
OS : Darwin
OS-release : 23.6.0
Version : Darwin Kernel Version 23.6.0: Fri Jul 5 17:56:39 PDT 2024; root:xnu-10063.141.1~2/RELEASE_ARM64_T8122
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.3
numpy : 2.2.6
pytz : 2025.2
dateutil : 2.9.0.post0
pip : None
Cython : None
sphinx : None
IPython : 9.2.0
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
html5lib : None
hypothesis : 6.131.23
gcsfs : None
jinja2 : 3.1.6
lxml.etree : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 20.0.0
pyreadstat : None
pytest : 8.3.5
python-calamine : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlsxwriter : None
zstandard : None
tzdata : 2025.2
qtpy : None
pyqt5 : None