BUG: pd.concat does not maintain timestamp[s][pyarrow] index type. (MultiIndex)

[randolf-scholz]

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

schema = {
    "id"    : "int64[pyarrow]",
    "time"   : "timestamp[s][pyarrow]",
    "value"  : "float[pyarrow]",
}  # fmt: skip
dfA = (
    pd.DataFrame(
        [
            (0, "2021-01-01 00:00:00", 5.3),
            (1, "2021-01-01 00:01:00", 5.4),
            (2, "2021-01-01 00:01:00", 5.4),
            (3, "2021-01-01 00:02:00", 5.5),
        ],
        columns=schema,
    )
    .astype(schema)
    .set_index(["id", "time"])
)
dfB = (
    pd.DataFrame(
        [
            (1, "2022-01-01 08:00:00", 6.3),
            (2, "2022-01-01 08:01:00", 6.4),
            (3, "2022-01-01 08:02:00", 6.5),
        ],
        columns=schema,
    )
    .astype(schema)
    .set_index(["id", "time"])
)
df = pd.concat([dfA, dfB], keys=[0, 1], names=["run"])
print(df.index.dtypes)  # ❌ time: object

Issue Description

The time index type gets coerced to object.

Expected Behavior

concat should maintain the dtype, since all concatenated tables have the same schema.

Installed Versions

INSTALLED VERSIONS

commit : d9cdd2e
python : 3.11.7.final.0
python-bits : 64
OS : Linux
OS-release : 6.5.0-28-generic
Version : #29~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Thu Apr 4 14:39:20 UTC 2
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8
pandas : 2.2.2
numpy : 1.26.4
pytz : 2024.1
dateutil : 2.9.0.post0
setuptools : 69.5.1
pip : 24.0
Cython : None
pytest : 8.1.1
hypothesis : 6.100.1
sphinx : 7.3.7
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.3
IPython : 8.23.0
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.3
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2024.3.1
gcsfs : None
matplotlib : 3.8.4
numba : None
numexpr : None
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 16.0.0
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.13.0
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2024.1
qtpy : None
pyqt5 : None