BUG: melt no longer supports id_vars and value_vars collapsing levels accross MultiIndex

[mark-thm]

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

period1 = pd.Period("2018Q1")
df = pd.DataFrame(
    [[1.0]],
    index=pd.PeriodIndex([period1, period1], name="period"),
    columns=pd.MultiIndex.from_tuples(
        [("a", "b")],
        names=["x", "y"],
    ),
)

pd.melt(df, id_vars=["a"])

Issue Description

Starting in 2.2.0, pd.melt claims that columns referenced in id_vars or value_vars are not present in a MultiIndex:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "venv/lib/python3.11/site-packages/pandas/core/reshape/melt.py", line 74, in melt
    raise KeyError(
KeyError: "The following id_vars or value_vars are not present in the DataFrame: ['a']"

Expected Behavior

Prior to 2.2.0, pd.melt melts the dataframe.

It appears the behavior was changed in this commit: https://github.com/pandas-dev/pandas/pull/55948/files#diff-a851c9e0a30604de55d051b077b0d9d2ab92d2386863991a2a4cb4444f103bffL44-L50

Installed Versions

INSTALLED VERSIONS

commit : fd3f571
python : 3.11.7.final.0
python-bits : 64
OS : Darwin
OS-release : 23.3.0
Version : Darwin Kernel Version 23.3.0: Wed Dec 20 21:30:44 PST 2023; root:xnu-10002.81.5~7/RELEASE_ARM64_T6000
machine : x86_64
processor : i386
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.0
numpy : 1.26.4
pytz : 2024.1
dateutil : 2.8.2
setuptools : 69.1.0
pip : 23.2.1
Cython : None
pytest : 8.0.1
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 5.1.0
html5lib : 1.1
pymysql : 1.4.6
psycopg2 : None
jinja2 : 3.1.3
IPython : 8.9.0
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.3
bottleneck : 1.3.7
dataframe-api-compat : None
fastparquet : None
fsspec : 2024.2.0
gcsfs : 2024.2.0
matplotlib : 3.8.3
numba : 0.59.0
numexpr : 2.9.0
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 15.0.0
pyreadstat : None
python-calamine : None
pyxlsb : 1.0.10
s3fs : 2024.2.0
scipy : 1.12.0
sqlalchemy : None
tables : None
tabulate : None
xarray : 2024.2.0
xlrd : None
zstandard : None
tzdata : 2024.1
qtpy : None
pyqt5 : None

[phofl]

cc @mroeschke

[Bassix9]

I kindly want to ask when this issue will be solved.

My working setup: Python 3.11.9 and pandas==2.0.3
Failing on Python 3.13.2 and pandas==2.2.3

The "Reproducible Example" doesn't work for me at all, but the error message of my app is the same. Thus, I assume the same root cause.