BUG: Index.sort_values with natsort key

[speleo3]

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 natsort
pd.Index([1, 3, 2]).sort_values(key=natsort.natsort_key)

Issue Description

Natural sorting works as expected with Series:

pd.Series([1, 3, 2]).sort_values(key=natsort.natsort_key)

Expecting that Index behaves the same, but it raises an exception:

pd.Index([1, 3, 2]).sort_values(key=natsort.natsort_key)
# TypeError: nargsort does not support MultiIndex. Use index.sort_values instead.

Expected Behavior

Expecting that key=natsort_key works the same in Index.sort_values and Series.sort_values.

As a workaround, this works, but seems unnecessarily verbose:

pd.Index([1, 3, 2]).sort_values(key=lambda v: pd.Index(natsort.natsort_key(v), tupleize_cols=False))

Installed Versions

INSTALLED VERSIONS
------------------
commit              : 9aa176687c04227af1c645712ea73296861858a3
python              : 3.10.13.final.0
python-bits         : 64
OS                  : Linux
OS-release          : 6.6.1-arch1-1
Version             : #1 SMP PREEMPT_DYNAMIC Wed, 08 Nov 2023 16:05:38 +0000
machine             : x86_64
processor           : 
byteorder           : little
LC_ALL              : None
LANG                : en_US.UTF-8
LOCALE              : en_US.UTF-8
pandas              : 2.2.0.dev0+651.g9aa176687c
numpy               : 1.26.0
pytz                : 2023.3.post1
dateutil            : 2.8.2
setuptools          : 68.2.2
pip                 : 23.3.1
Cython              : 3.0.5
pytest              : 7.4.3
hypothesis          : 6.90.0
sphinx              : 6.2.1
blosc               : None
feather             : None
xlsxwriter          : 3.1.9
lxml.etree          : 4.9.3
html5lib            : 1.1
pymysql             : 1.4.6
psycopg2            : 2.9.7
jinja2              : 3.1.2
IPython             : 8.17.2
pandas_datareader   : None
bs4                 : 4.12.2
bottleneck          : 1.3.7
dataframe-api-compat: None
fastparquet         : 2023.10.1
fsspec              : 2023.10.0
gcsfs               : 2023.10.0
matplotlib          : 3.8.1
numba               : 0.58.1
numexpr             : 2.8.7
odfpy               : None
openpyxl            : 3.1.2
pandas_gbq          : None
pyarrow             : 14.0.1
pyreadstat          : 1.2.4
python-calamine     : None
pyxlsb              : 1.0.10
s3fs                : 2023.10.0
scipy               : 1.11.3
sqlalchemy          : 2.0.23
tables              : 3.9.1
tabulate            : 0.9.0
xarray              : 2023.11.0
xlrd                : 2.0.1
zstandard           : 0.22.0
tzdata              : 2023.3
qtpy                : None
pyqt5               : None

[hvsesha]

@speleo3 I found out the issue here
@Dhayanidhi-M Thanks for your help
In Sorting.py
Nargsort function casting is the problem

#56081 BugFix Casting
#items = ensure_key_mapped(items, key)
items=cast(items, ensure_key_mapped(items, key))._values

cast(type(items),ensure_key_mapped(items, key))._values
Kindly check and revert back

[bdwzhangumich]

take

[yuanx749]

The problem is that applying natsort.natsort_key to Index results in MultiIndex.