BUG: select_dtypes does not work with timestamp[ns][pyarrow]

[dbalabka]

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 pyarrow

# Create a sample DataFrame
data = {
    'id': [1, 2, 3],
    'date1': pd.to_datetime(['2023-01-01', '2023-01-02', '2023-01-03']),
    'date2': pd.to_datetime(['2023-02-01', '2023-02-02', '2023-02-03']),
    'value': [10, 20, 30]
}

df = pd.DataFrame(data)

# Convert datetime columns to 'timestamp[ns][pyarrow]'
df = df.astype({
    'date1': 'timestamp[ns][pyarrow]',
    'date2': 'timestamp[ns][pyarrow]',
    'value': 'int64[pyarrow]'
})

print('\n\nAll types:\n' + str(df.dtypes))
print('\n\nIt works for other types `int64`:\n' + str(df.select_dtypes(include=['int64']).dtypes))
print('\n\nIt works for other types `pd.ArrowDtype(pa.int64())`:\n' + str(df.select_dtypes(include=[pd.ArrowDtype(pa.int64())]).dtypes))
print('\n\nBut it does not for `timestamp[ns][pyarrow]`:\n'  + str(df.select_dtypes(include=['timestamp[ns][pyarrow]']).dtypes))
print('\n\nThe type should not interpreter as `datetime64[ns]`:\n'  + str(df.select_dtypes(include=['datetime64[ns]']).dtypes))
print('\n\nHere is a proper workaround with `pd.ArrowDtype(pa.timestamp(ns))`:\n'  + str(df.select_dtypes(include=[pd.ArrowDtype(pa.timestamp('ns'))]).dtypes))

All types:
id                        int64
date1    timestamp[ns][pyarrow]
date2    timestamp[ns][pyarrow]
value            int64[pyarrow]
dtype: object

It works for other types `int64`:
id                int64
value    int64[pyarrow]
dtype: object

It works for other types `pd.ArrowDtype(pa.int64())`:
id                int64
value    int64[pyarrow]
dtype: object

But it does not for `timestamp[ns][pyarrow]`:
Series([], dtype: object)

The type should not interpreter as `datetime64[ns]`:
date1    timestamp[ns][pyarrow]
date2    timestamp[ns][pyarrow]
dtype: object

Here is a proper workaround with `pd.ArrowDtype(pa.timestamp(ns))`:
date1    timestamp[ns][pyarrow]
date2    timestamp[ns][pyarrow]
dtype: object

Issue Description

For unknown reasons, select_dtypes can not select the timestamp[ns][pyarrow] type because of the incorrect string-representation to type object conversion. It does work when we use type object explicitly like: pd.ArrowDtype(pa.timestamp('ns'))

Expected Behavior

select_dtypes should select columns with timestamp[ns][pyarrow] type when timestamp[ns][pyarrow] string provided.
select_dtypes should select columns with timestamp[ns][pyarrow] type when pd.ArrowDtype(pa.timestamp(ns)) object provided.
select_dtypes should not select columns with timestamp[ns][pyarrow] when datetime64[ns] provided.

Installed Versions

INSTALLED VERSIONS

commit : d9cdd2e
python : 3.10.12.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.153.1-microsoft-standard-WSL2
Version : #1 SMP Fri Mar 29 23:14:13 UTC 2024
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : en_US.UTF-8
pandas : 2.2.2
numpy : 1.26.3
pytz : 2023.4
dateutil : 2.8.2
setuptools : 69.0.3
pip : 24.0
Cython : None
pytest : 7.4.4
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.3
IPython : 8.20.0
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.3
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2023.12.2
gcsfs : 2023.12.2post1
matplotlib : 3.8.2
numba : 0.58.1
numexpr : None
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 14.0.2
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : 2023.12.2
scipy : 1.12.0
sqlalchemy : 2.0.29
tables : None
tabulate : 0.9.0
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.4
qtpy : None
pyqt5 : None

[dbalabka]

Related to the following line:

pandas/pandas/core/frame.py

Line 4895 in 2cdb97e

dtype = dtype if not isinstance(dtype, ArrowDtype) else dtype.numpy_dtype

The following line should not return the timestamp[ns][pyarrow] types:

df.select_dtypes(include=['datetime64[ns]'])

Here is a proper workaround: avoid using string representation of the type and provide object type explicitly:

df.select_dtypes(include=[pd.ArrowDtype(pa.timestamp('ns'))])

[dbalabka]

it looks related to #52577

// cc @phofl

[yuanx749]

Seems it does not work with other pyarrow string representation either:

print(df.select_dtypes(include=['int64[pyarrow]']).dtypes)
# Series([], dtype: object)

[jacek-pliszka]

null has similar problem:
``In [10]: df = pd.DataFrame({"a": [None], "b": [[1]]}).convert_dtypes(dtype_backend="pyarrow")

In [11]: df.dtypes
Out[11]:
a null[pyarrow]
b object
dtype: object

In [12]: df.select_dtypes(include=['object'])
Out[12]:
a b
0 None [1]