BUG: `RollingGroupby.agg` returns no columns when column selected in list is one of the groupby columns

[hsorsky]

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

X = pd.DataFrame({"group": [1, 2, 2, 3, 3, 3], "other": [1, 1, 1, 1, 1, 1]})
X.groupby(["group"])[["group"]].rolling(2, min_periods=1).agg("count")

Issue Description

A DataFrame with no columns is returned.

Empty DataFrame
Columns: []
Index: [(1, 0), (2, 1), (2, 2), (3, 3), (3, 4), (3, 5)]

---

As an FYI, X.groupby(["group"])["group"].rolling(2, min_periods=1).agg("count") seems fine

group   
1      0    1.0
2      1    1.0
       2    2.0
3      3    1.0
       4    2.0
       5    2.0
Name: group, dtype: float64

as does
X.groupby(["group"])[["other"]].rolling(2, min_periods=1).agg("count")

         other
group         
1     0    1.0
2     1    1.0
      2    2.0
3     3    1.0
      4    2.0
      5    2.0

as does
X.groupby(["group"])["other"].rolling(2, min_periods=1).agg("count")

group   
1      0    1.0
2      1    1.0
       2    2.0
3      3    1.0
       4    2.0
       5    2.0
Name: other, dtype: float64

---

Also, the problem does not seem to persist if we don't perform a non collapsing aggregation:

X.groupby(["group"])[["group"]].agg("count")

       group
group       
1          1
2          2
3          3

but does if we perform expanding aggregation:

X.groupby(["group"])[["group"]].expanding(min_periods=1).agg("count")

Empty DataFrame
Columns: []
Index: [(1, 0), (2, 1), (2, 2), (3, 3), (3, 4), (3, 5)]

Expected Behavior

It would output the same as when one does

X.groupby(["group"])[["other"]].rolling(2, min_periods=1).agg("count")

but with "group" as the column name.

Installed Versions

INSTALLED VERSIONS
------------------
commit              : a671b5a8bf5dd13fb19f0e88edc679bc9e15c673
python              : 3.10.11.final.0
python-bits         : 64
OS                  : Darwin
OS-release          : 22.4.0
Version             : Darwin Kernel Version 22.4.0: Mon Mar  6 20:59:28 PST 2023; root:xnu-8796.101.5~3/RELEASE_ARM64_T6000
machine             : arm64
processor           : arm
byteorder           : little
LC_ALL              : None
LANG                : en_US.UTF-8
LOCALE              : en_US.UTF-8

pandas              : 2.1.4
numpy               : 1.26.3
pytz                : 2023.3.post1
dateutil            : 2.8.2
setuptools          : 65.5.0
pip                 : 23.0.1
Cython              : None
pytest              : None
hypothesis          : None
sphinx              : None
blosc               : None
feather             : None
xlsxwriter          : None
lxml.etree          : None
html5lib            : None
pymysql             : None
psycopg2            : None
jinja2              : None
IPython             : 8.19.0
pandas_datareader   : None
bs4                 : None
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              : 2023.4
qtpy                : None
pyqt5               : None

[rhshadrach]

Thanks for the report, related to #40341 (comment) (cc @mroeschke, @jbrockmendel).

The rest of groupby will keep the grouping column if you select it, e.g.

df[["a", "b"]].groupby("a")[["a", "b"]].sum()

will sum both a and b in the result. I think we should agree with that here.