BUG: Floordiv with integral pyarrow types should avoid storing results in floating type for intermediate calculation

[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

This issue only occurs on main (not in any released version).

>>> a = pd.Series([18014398509481983], dtype="int64[pyarrow]")
>>> a // 1
0    18014398509481984
dtype: int64[pyarrow]
>>>

Issue Description

Expected result is 18014398509481983.

Expected Behavior

Behavior with numpy types:

>>> a = pd.Series([18014398509481983], dtype="int64")
>>> a // 1
0    18014398509481983
dtype: int64
>>>

Installed Versions

INSTALLED VERSIONS

commit : f0b61c5
python : 3.11.4.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.22631
machine : AMD64
processor : Intel64 Family 6 Model 151 Stepping 2, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United States.1252

pandas : 2.1.0.dev0+2318.gf0b61c5618
numpy : 1.26.2
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 68.2.2
pip : 23.3.1
Cython : 3.0.5
pytest : 7.4.3
hypothesis : 6.91.0
sphinx : 6.2.1
blosc : 1.11.1
feather : None
xlsxwriter : 3.1.9
lxml.etree : 4.9.3
html5lib : 1.1
pymysql : 1.4.6
psycopg2 : 2.9.9
jinja2 : 3.1.2
IPython : 8.18.1
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.2
bottleneck : 1.3.7
dataframe-api-compat : None
fastparquet : 2023.10.1
fsspec : 2023.12.0
gcsfs : 2023.12.0
matplotlib : 3.8.2
numba : 0.58.1
numexpr : 2.8.7
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 14.0.1
pyreadstat : 1.2.5
python-calamine : None
pyxlsb : 1.0.10
s3fs : 2023.12.0
scipy : 1.11.4
sqlalchemy : 2.0.23
tables : 3.9.2
tabulate : 0.9.0
xarray : 2023.11.0
xlrd : 2.0.1
zstandard : 0.22.0
tzdata : 2023.3
qtpy : None
pyqt5 : None