BUG: Floordiv with arrow types rounds towards 0 instead of negative infinity

[rohanjain101]

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

>>> a = pd.Series([-7], dtype="int64[pyarrow]")
>>> b = pd.Series([4], dtype="int64[pyarrow]")
>>> a // b
0   -1
dtype: int64[pyarrow]
>>>

Issue Description

Expected result is -2.

Expected Behavior

>>> -7 // 4
-2
>>>

Expected is same behavior as python floordiv (rounding towards negative infinity, not 0). Floordiv with numpy types also matches this behavior:

>>> a = pd.Series([-7])
>>> b = pd.Series([4])
>>> a // b
0   -2
dtype: int64
>>>

Installed Versions

INSTALLED VERSIONS

commit : e86ed37
python : 3.11.2.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.22621
machine : AMD64
processor : Intel64 Family 6 Model 85 Stepping 7, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United States.1252

pandas : 2.1.1
numpy : 1.25.2
pytz : 2023.3
dateutil : 2.8.2
setuptools : 68.0.0
pip : 23.2.1
Cython : None
pytest : 7.0.1
hypothesis : None
sphinx : 4.2.0
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.14.0
pandas_datareader : None
bs4 : 4.12.2
bottleneck : None
dataframe-api-compat: None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 13.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : 0.9.0
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None