BUG: str.fullmatch behavior is not the same for object dtype and string[pyarrow] dtype

[ptth222]

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Reproducible Example

import pandas

test_series = pandas.Series(['asdf', 'as'], dtype='string[pyarrow]')
regex = r'((as)|(as))'
regex2 = r'(as)|(as)'

test_series.str.fullmatch(regex)
# False
# True
test_series.str.fullmatch(regex2)
# True
# True

test_series2 = pandas.Series(['asdf', 'as'], dtype=str)

test_series2.str.fullmatch(regex)
# False
# True
test_series2.str.fullmatch(regex2)
# False
# True

Issue Description

As the example shows you can use the same regular expression for the str.fullmatch method when using a str dtype and string[pyarrow] dtype and get different results. This seems to stem from Apache Arrow not having a dedicated fullmatch or match, so the regular expression has to be edited with "^" and "$" characters before being delivered to its search function. There might also be some special handling in Python's fullmatch method with the "|" operator. Long story short, at least some regular expressions delivered to PyArrow need additional surrounding parentheses to get the same fullmatch results as when using Python's fullmatch.

I have submitted #61073 to try and address this.

Expected Behavior

The second set of fullmatch results in the example shows the expected behavior. The str.fullmatch method should behave the same for either dtype.

Installed Versions

INSTALLED VERSIONS

commit : 0691c5c
python : 3.10.5
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19045
machine : AMD64
processor : Intel64 Family 6 Model 158 Stepping 12, GenuineIntel
byteorder : little
LC_ALL : None
LANG : en
LOCALE : English_United States.1252

pandas : 2.2.3
numpy : 1.24.4
pytz : 2022.1
dateutil : 2.8.2
pip : 25.0.1
Cython : 3.0.11
sphinx : 5.1.1
IPython : 8.21.0
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
html5lib : 1.1
hypothesis : None
gcsfs : None
jinja2 : None
lxml.etree : 4.9.1
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : 3.1.4
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 19.0.1
pyreadstat : None
pytest : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : 2.0.9
tables : None
tabulate : 0.9.0
xarray : None
xlrd : None
xlsxwriter : 3.2.0
zstandard : None
tzdata : 2024.1
qtpy : 2.4.1
pyqt5 : None