BUG: rolling.groupby with on and __getitem__ doesn't mutate underlying object
- [x] closes #43355
- [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

Thanks @mroeschke This does not close the issue? (as indicated in the OP)

There are still the issues of the inconsistent indexes between `grp.count()` and `grp["y"].count()` and the issue of the change in index from 1.2.5? Sorry, since https://github.com/pandas-dev/pandas/issues/43355 reported 2 bugs, this just addresses one of them.

I just opened up https://github.com/pandas-dev/pandas/issues/43405 separately since this PR does not address the `index` inconsistency. > I just opened up #43405 separately since this PR does not address the `index` inconsistency.

Thanks @mroeschke 

> There are still the issues of the inconsistent indexes between `grp.count()` and `grp["y"].count()` and the issue of the change in index from 1.2.5?

there was a typo here. the index didn't change from 1.2.5, the result columns did. There was a change in index from 1.1.5. I've commented on the issue. https://github.com/pandas-dev/pandas/issues/43405#issuecomment-913105340 thanks @mroeschke 