BUG: Series.groupby.rolling duplicates  index when grouping over index
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [x] (optional) I have confirmed this bug exists on the master branch of pandas.

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#### Code Sample, a copy-pastable example

```python
data = {
    'groupby_col': ['A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', ],
    'agg_col': [1, 1, 0, 1, 0, 0, 0, 0, 1, 0],
}
df = pd.DataFrame(data).set_index("groupby_col")
grouped = df.groupby('groupby_col')
rolled = grouped.rolling(4)

result = rolled.mean()
print(result)

```
Output:
```
                         agg_col
groupby_col groupby_col         
A           A                NaN
            A                NaN
            A                NaN
            A               0.75
            A               0.50
B           B                NaN
            B                NaN
            B                NaN
            B               0.25
            B               0.25
```

#### Problem description

The duplicate ``groupby_col`` seems at least odd.

...

#### Expected Output

Would expect, that we get ``groupby_col`` only once in the index and a ``Series`` instead of a ``DataFrame``

Maybe related to #36507, but

```
data = {
    'groupby_col': ['A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', ],
    'agg_col': [1, 1, 0, 1, 0, 0, 0, 0, 1, 0],
}
df = pd.DataFrame(data).set_index("groupby_col")
grouped = df.groupby('groupby_col')
result = grouped.apply(sum)
print(result)
```
works. So I am not sure.

#### Output of ``pd.show_versions()``

<details>

master

</details>
