BUG: read_csv losing precision when reading Int64[pyarrow] data with N/A values

[MarcoGorelli]

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
import numpy as np
from io import StringIO
TESTDATA1 = StringIO("""col1;col2
     1;123
     2;456
     3;1582218195625938945
     """)
TESTDATA2 = StringIO("""col1;col2
     1;123
     2;
     3;1582218195625938945
     """)
D1 = pd.read_csv(TESTDATA1, sep=";", dtype={'col2':'Int64[pyarrow]'})
D2 = pd.read_csv(TESTDATA2, sep=";", dtype={'col2':'Int64[pyarrow]'})
D1['col2']
D2['col2']
D1.loc[2,'col2'] == D2.loc[2,'col2']

Issue Description

This yields

In [51]: D1['col2']
Out[51]:
0                    123
1                    456
2    1582218195625938945
Name: col2, dtype: int64[pyarrow]

In [52]: D2['col2']
Out[52]:
0                    123
1                   <NA>
2    1582218195625938688
Name: col2, dtype: int64[pyarrow]

Expected Behavior

they should be the same

Installed Versions

INSTALLED VERSIONS

commit : 1c606d5
python : 3.10.12.final.0
python-bits : 64
OS : Linux
OS-release : 5.10.102.1-microsoft-standard-WSL2
Version : #1 SMP Wed Mar 2 00:30:59 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_GB.UTF-8
LOCALE : en_GB.UTF-8

pandas : 2.2.0.dev0+694.g1c606d5f01
numpy : 1.25.1
pytz : 2023.3
dateutil : 2.8.2
setuptools : 67.6.1
pip : 23.1.2
Cython : None
pytest : 7.3.1
hypothesis : 6.82.4
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.16.1
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.2
bottleneck : None
dataframe-api-compat : None
fastparquet : 2023.7.0
fsspec : 2023.6.0
gcsfs : None
matplotlib : 3.7.1
numba : 0.58.1
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 12.0.1
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.11.0
sqlalchemy : 2.0.20
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None