BUG: Series.str.replace stopped working with regex groups

[worc4021]

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
from re import sub

teststr = "var.one[0]"
print(sub(r'\[(\d+)\]',r'(\1)',teststr))

s = pd.Series(["var.one[0]", "var.two[1]", "var.three[2]"]).convert_dtypes(dtype_backend="pyarrow")

t = s.str.replace(r'\[(\d+)\]',r'(\1)',regex=True)

print(t)

Issue Description

The most recent pandas version produces the following error message:

var.one(0)
Traceback (most recent call last):
  File "/workspaces/verbose-system/testfile.py", line 9, in <module>
    t = s.str.replace(r'\[(\d+)\]',r'(\1)',regex=True)
        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/workspaces/verbose-system/.new/lib/python3.12/site-packages/pandas/core/strings/accessor.py", line 140, in wrapper
    return func(self, *args, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/workspaces/verbose-system/.new/lib/python3.12/site-packages/pandas/core/strings/accessor.py", line 1580, in replace
    result = self._data.array._str_replace(
             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/workspaces/verbose-system/.new/lib/python3.12/site-packages/pandas/core/arrays/_arrow_string_mixins.py", line 182, in _str_replace
    raise NotImplementedError(
NotImplementedError: replace is not supported with a re.Pattern, callable repl, case=False, flags!=0, or when the replacement string contains named group references (\g<...>, \d+)

I have trialed all possible combinations of \1, \g<1>, named groups, precompiled patterns, etc. However, this issue persists. I believe that this is related to: #57636

Expected Behavior

With pandas 2.3.0 the output of the script above was:

var.one(0)
0      var.one(0)
1      var.two(1)
2    var.three(2)
dtype: string[pyarrow]

Installed Versions

INSTALLED VERSIONS
------------------
commit                : 9c8bc3e55188c8aff37207a74f1dd144980b8874
python                : 3.12.11
python-bits           : 64
OS                    : Linux
OS-release            : 6.8.0-1030-azure
Version               : #35~22.04.1-Ubuntu SMP Mon May 26 18:08:30 UTC 2025
machine               : x86_64
processor             : 
byteorder             : little
LC_ALL                : None
LANG                  : C.UTF-8
LOCALE                : C.UTF-8

pandas                : 2.3.3
numpy                 : 2.3.3
pytz                  : 2025.2
dateutil              : 2.9.0.post0
pip                   : 25.0.1
Cython                : None
sphinx                : None
IPython               : None
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            : None
gcsfs                 : None
jinja2                : None
lxml.etree            : None
matplotlib            : None
numba                 : None
numexpr               : None
odfpy                 : None
openpyxl              : None
pandas_gbq            : None
psycopg2              : None
pymysql               : None
pyarrow               : 21.0.0
pyreadstat            : None
pytest                : None
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