BUG: pd.concat changes multiindex dtype of string to object

[dalejung]

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

# create two frames with [string, Int64] multi index.
mi_df = pd.DataFrame({
    'strings': ['HELLO FREN'],
    'ints': [0],
    'floats': [0.1],
}).convert_dtypes().set_index(['strings', 'ints'])

# print(mi_df.index.dtypes)
# strings    string[python]
# ints                Int64

mi_df2 = pd.DataFrame({
    'strings': ['BYE FREN'],
    'ints': [1],
    'floats': [0.1],
}).convert_dtypes().set_index(['strings', 'ints'])

# print(mi_df2.index.dtypes)
# strings    string[python]
# ints                Int64

# concatting index where strings are same retains dtype
good_concat = pd.concat([mi_df, mi_df.copy()])
assert good_concat.index.dtypes['strings'] == 'string'

# otherwise the string level gets turned into object
bad_concat = pd.concat([mi_df, mi_df2])
# ERROR: this should be 'string' and not object.
assert bad_concat.index.dtypes['strings'] == object
# print(bad_concat.index.dtypes)
# strings    object
# ints        Int64

Issue Description

Regression found on main. The dtypes of the MultiIndex shouldn't change in a concat with identical index dtypes.

This works as expected on 1.5.3.

Expected Behavior

Dtypes remain unchanged in concatenated frame.

Installed Versions

INSTALLED VERSIONS

commit : 8db9f11ed3d87310ae46fe77ad89041973a4893d
python : 3.11.3.final.0
python-bits : 64
OS : Linux
OS-release : 6.4.9-arch1-1
Version : #1 SMP PREEMPT_DYNAMIC Tue, 08 Aug 2023 22:14:05 +0000
machine : x86_64
processor :
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.1.0rc0+97.g8db9f11ed3
numpy : 1.24.3
pytz : 2023.3
dateutil : 2.8.2
setuptools : 65.3.0
pip : 22.2.2
Cython : 0.29.33
pytest : 7.4.0
hypothesis : 6.47.1
sphinx : 6.2.1
blosc : 1.11.1
feather : None
xlsxwriter : 3.1.0
lxml.etree : 4.9.2
html5lib : 1.1
pymysql : 1.0.3
psycopg2 : 2.9.6
jinja2 : 3.1.2
IPython : 8.15.0.dev
pandas_datareader : None
bs4 : 4.12.2
bottleneck : 1.3.7
dataframe-api-compat: None
fastparquet : 2023.4.0
fsspec : 2023.5.0
gcsfs : 2023.5.0
matplotlib : 3.7.1
numba : 0.57.0
numexpr : 2.8.4
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 14.0.0.dev14+g72811b13e
pyreadstat : 1.2.1
pyxlsb : 1.0.10
s3fs : 2023.5.0
scipy : 1.10.1
sqlalchemy : 2.0.14
tables : 3.8.0
tabulate : 0.9.0
xarray : 2023.5.0
xlrd : 2.0.1
zstandard : 0.21.0
tzdata : 2023.3
qtpy : None
pyqt5 : None

[phofl]

Does this work on 2.0 as well?

[dalejung]

In [9]: bad_concat.index.dtypes
Out[9]:
strings    string[python]
ints                Int64
dtype: object

In [10]: print(pd.__version__)
2.0.3

Works as expected in 2.0.3.

[phofl]

Thx