BUG: Groupby ops on empty objects loses index, columns, dtypes
- [x] closes #26411
- [x] closes #13483
- [x] tests added / passed
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [x] whatsnew entry

@jreback - thanks, whatsnew and test have been updated.