BUG: Unable to use CustomBusinessDays in a MultiIndex

[cokelid]

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Reproducible Example

import pandas as pd

bus_day = pd.offsets.CustomBusinessDay(holidays=['2023-07-04'])  # Mon-Fri except July 4th

dates = pd.date_range('2023-07-03', '2023-07-06', freq=bus_day)
df1 = pd.DataFrame({'col1': [300, 500, 600]}, index=dates)
print(df1.index.freq.holidays)  # Can get freq from dataframe index

mi = pd.MultiIndex.from_product([dates, ('foo','bar')])
df2 = pd.DataFrame({'col1': [300, 301, 500, 501, 600, 601]}, index=mi)
print(df2.index.get_level_values(0).freq)  # Gives None. Freq lost from dataframe multi-index

periods = pd.period_range('2023-07-03', '2023-07-06', freq=bus_day)  # Try PeriodIndex?
# Gives: TypeError: CustomBusinessDay cannot be used with Period or PeriodDtype

Issue Description

I can use a CustomBusinessDay frequency in a DatetimeIndex and retrieve the frequency from the .index of a dataframe.

If I use a DatetimeIndex in a MultiIndex, then I lose the freq from the level of the index.

I note the freq does persist in a PeriodIndex within a MultiIndex, but you can't use a CustomBusinessDay in a PeriodIndex as shown.

Expected Behavior

I would like the Datetime level of the MultiIndex to show the orginial freq:
print(df2.index.get_level_values(0).freq) would give <CustomBusinessDay>

Installed Versions

INSTALLED VERSIONS ------------------ commit : a671b5a python : 3.10.13.final.0 python-bits : 64 OS : Linux OS-release : 5.15.145.2-1.cm2 Version : #1 SMP Wed Jan 17 15:39:07 UTC 2024 machine : x86_64 processor : x86_64 byteorder : little LC_ALL : en_US.UTF-8 LANG : en_US.UTF-8 LOCALE : en_US.UTF-8

pandas : 2.1.4
numpy : 1.26.4
pytz : 2024.1
dateutil : 2.9.0.post0
setuptools : 65.5.0
pip : 24.0
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.3
IPython : 8.22.2
pandas_datareader : None
bs4 : 4.12.3
bottleneck : None
dataframe-api-compat: None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2024.1
qtpy : None
pyqt5 : None

[dontgoto]

This loss of information does happen with the DateTimeIndex and not with the PeriodIndex. Reason is that the freqis an attribute of each value in the PeriodIndex. With the DateTimeIndex, the freq, etc. get lost when calling get_level_values(), due to the shallow copying logic.

The DateTimeIndex is the only index type with this edge case.

[cokelid]

Thanks. Is this the shallow copy you're referring to?
return lev._shallow_copy(filled, name=name)