BUG: Series.apply with arrow integral types passes nan instead of pd.NA for missing values to udf

[rohanjain101]

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Reproducible Example

>>> s = pd.Series([1, None], dtype="int16[pyarrow]")
>>> def my_udf(value):
...     return str(value)
...
>>> s.apply(my_udf)
0    1.0
1    nan
dtype: object
>>>

Issue Description

NaN is passed to udf instead of pd.NA, NaN should be impossible for integral type to hold

Expected Behavior

Expected behavior is behavior from pandas 2.1.4:

>>> s = pd.Series([1, None], dtype="int16[pyarrow]")
>>> def my_udf(value):
...     return str(value)
...
>>> s.apply(my_udf)
0       1
1    <NA>
dtype: object
>>>

UDF receives pd.NA instead of NaN

Installed Versions

INSTALLED VERSIONS

commit : d4c8d82
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 : 2.2.0rc0
numpy : 1.26.2
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 69.0.2
pip : 23.3.1
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 : 8.19.0
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.2
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : 3.8.2
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 14.0.0
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.11.4
sqlalchemy : None
tables : None
tabulate : 0.9.0
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[rohanjain101]

Based on discussion in #56290, it seems it may be an intentional change in 2.2.x compared to 2.1.x.

[rohanjain101]

>>> pd.Series(map(my_udf, s))
0       1
1    <NA>
dtype: object
>>>

This gives the expected result, it seems a bit odd, that using apply would give a different result and call the udf with different values.

[phofl]

Yes this was indeed an intentional change to get rid of the annoying behaviour of converting to NumPy object all the time