ENH: Allow as_index=False on SeriesGroupBy
Would make the code:

    s.to_frame(s.name).groupby(groups, as_index=False).sum()

Become:

    s.groupby(groups, as_index=False).sum()

The change should just amount to calling a function like:

```
def adjust_for_as_index(self, result: FrameOrSeries) -> DataFrame:
    if result.ndim == 1:
        result = result.to_frame(result.name)
    self._insert_inaxis_grouper_inplace(result)
    result.index = np.arange(len(result))
```

in various methods of SeriesGroupBy (and could be used in DataFrameGroupBy).

This would close #13666 and make #35443 to be just about error reporting for the `axis=1` case.