BUG: Pyarrow implementation of str.fullmatc matches partial string

[sjnarmstrong]

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 pyarrow as pa
import pandas as pd
print("pd Version: ", pd.__version__, "pa Version: ",  pa.__version__)
print(
    "Pyarrow Implementation:", pd.Series(["test$test"], dtype=pd.ArrowDtype(pa.string())).str.fullmatch("test\\$").values[0],
    "\nNative Implementation:", pd.Series(["test$test"]).str.fullmatch("test\\$").values[0]
)
# pd Version:  2.1.2 pa Version:  14.0.2
# Pyarrow Implementation: True 
# Native Implementation: False

Issue Description

Fullmatch with pattern ending in "$" on pyarrow implementation can match a partial string. Expected the pyarrow and the native implementation to match. It appears that the "//$" in the following line should be a "\$"

pandas/pandas/core/arrays/arrow/array.py

Line 2274 in 62dbbe6

if not pat.endswith("$") or pat.endswith("//$"):

Expected Behavior

A fullmatch on a pattern ending with "$" should not allow a partial match

Installed Versions

INSTALLED VERSIONS

commit : a60ad39
python : 3.11.4.final.0
python-bits : 64
OS : Darwin
OS-release : 23.0.0
Version : Darwin Kernel Version 23.0.0: Fri Sep 15 14:43:05 PDT 2023; root:xnu-10002.1.13~1/RELEASE_ARM64_T6020
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : None
LOCALE : None.UTF-8

pandas : 2.1.2
numpy : 1.26.1
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 65.5.0
pip : 23.1.2
Cython : None
pytest : 7.4.3
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.17.2
pandas_datareader : None
bs4 : 4.12.2
bottleneck : None
dataframe-api-compat: None
fastparquet : None
fsspec : 2023.12.1
gcsfs : None
matplotlib : 3.8.2
numba : None
numexpr : None
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 14.0.2
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.11.3
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[rhshadrach]

#51207 (comment)

cc @mroeschke @jbrockmendel

[rhshadrach]

This looks straightforward, tagging it as a good first issue.

[neha3004]

Created a pull request with the required changes: #56663

Please let me know in case of any issues.

[AYUSHMOHANTY10]

Assign this issue to me