BUG: df.groupby.apply(lambda x: x.reindex) behaviour changed from Pandas 1.3.0 to 1.3.3

[mlee94]

• 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 master branch of pandas.

Reproducible Example

import pandas as pd
import numpy as np

start_date = pd.to_datetime('2019-01-01')
end_date = pd.to_datetime('2019-01-05')
data = {
    'code': ['X333']*5,
    'date': pd.date_range(start_date, periods=5),
    'float': np.random.randn(5),
}

df = (
    pd.DataFrame(data)
    .set_index('date')
    .groupby('code')
    .apply(
        lambda x: x.reindex(pd.date_range(start_date, end_date, name='date'))
    )
)
print(df)

Issue Description

pandas=1.3.3
Group by key code is removed from the multi-index:

            code     float
date
2019-01-01  X333 -0.732025
2019-01-02  X333  0.251650
2019-01-03  X333  0.301808
2019-01-04  X333 -0.585017
2019-01-05  X333  0.067119

Expected Behavior

pandas=1.3.0
Group by key code is kept in the multi-index:

                 code     float
code date
X333 2019-01-01  X333 -0.971248
     2019-01-02  X333  0.701875
     2019-01-03  X333  1.222485
     2019-01-04  X333  0.315564
     2019-01-05  X333  0.836289

Installed Versions

INSTALLED VERSIONS

commit : 73c6825
python : 3.7.10.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19041
machine : AMD64
processor : Intel64 Family 6 Model 58 Stepping 0, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : None.None

pandas : 1.3.3
numpy : 1.21.2
pytz : 2021.1
dateutil : 2.8.2
pip : 21.2.4
setuptools : 58.0.4
Cython : None
pytest : 6.2.5
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : 3.0.1
lxml.etree : 4.6.3
html5lib : None
pymysql : None
psycopg2 : 2.9.1 (dt dec pq3 ext lo64)
jinja2 : 2.11.3
IPython : 7.27.0
pandas_datareader: None
bs4 : 4.10.0
bottleneck : None
fsspec : 2021.08.1
fastparquet : None
gcsfs : None
matplotlib : None
numexpr : None
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : 5.0.0
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : 1.4.24
tables : None
tabulate : None
xarray : 0.19.0
xlrd : None
xlwt : None
numba : 0.53.0

[TomAugspurger]

I think this is the same as #43568.