BUG: pd.Series.apply / pd.Series.map outputs to numpy dtype for a double[pyarrow] input

[VaasuDevanS]

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
s = pd.Series([10, 20, 30], dtype='double[pyarrow]')
s.apply(lambda x: x + 1)
s.map(lambda x: x + 1)

Issue Description

Using the series .apply() or .map() methods, the return dtype is float64

>>> print(s)
0    10.0
1    20.0
2    30.0
dtype: double[pyarrow]

>>> print(s.apply(lambda x: x + 1))
0    11.0
1    21.0
2    31.0
dtype: float64

>>> print(s.map(lambda x: x + 1))
0    11.0
1    21.0
2    31.0
dtype: float64

Expected Behavior

The return dtype is expected to be the same as the input. In this case it's double[pyarrow]

Installed Versions

INSTALLED VERSIONS

commit : 965ceca
python : 3.10.11.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.107+
Version : #1 SMP Sat Apr 29 09:15:28 UTC 2023
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.0.2
numpy : 1.22.4
pytz : 2022.7.1
dateutil : 2.8.2
setuptools : 67.7.2
pip : 23.1.2
Cython : 0.29.34
pytest : 7.2.2
hypothesis : None
sphinx : 3.5.4
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.9.2
html5lib : 1.1
pymysql : None
psycopg2 : 2.9.6
jinja2 : 3.1.2
IPython : 7.34.0
pandas_datareader: 0.10.0
bs4 : 4.11.2
bottleneck : None
brotli : None
fastparquet : None
fsspec : 2023.4.0
gcsfs : None
matplotlib : 3.7.1
numba : 0.56.4
numexpr : 2.8.4
odfpy : None
openpyxl : 3.0.10
pandas_gbq : 0.17.9
pyarrow : 9.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.10.1
snappy : None
sqlalchemy : 2.0.10
tables : 3.8.0
tabulate : 0.8.10
xarray : 2022.12.0
xlrd : 2.0.1
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[mroeschke]

Thanks for the report but this is essentially a duplicate of #51991 so closing in favor of that issue