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 datetime
import pandas as pd
import pyarrow as pa

df = pd.DataFrame([[42]], columns=["col"])
df["int16"] = pa.array([16], type=pa.int16())
df["date"] = pa.array([datetime.date(2024, 1, 1)], type=pa.date32())
df["string"] = pa.array(["foo"], pa.string())

Issue Description

>>> df.dtypes
col               int64
int16             int16
date      datetime64[s]
string           object
dtype: object

I am surprised that the pyarrow type is not maintained during assignment

Expected Behavior

>>> df.dtypes
col               int64
int16             int16[pyarrow]
date              date32[pyarrow]
string            string[pyarrow]
dtype: object

Installed Versions

on main