BUG: DataFrame.apply with result_type=reduce incorrect index
- [ ] closes #xxxx
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

This may xref #35683 pending discussion there.
looks ok to me, could put on 1.1.2 @jreback is this ready? and does this close #35683

test failures are known pyarrow related updated+green lgtm can you rebase rebased+green Owee, I'm MrMeeseeks, Look at me.

There seem to be a conflict, please backport manually. Here are approximate instructions:

1. Checkout backport branch and update it.

```
$ git checkout 1.1.x
$ git pull
```

2. Cherry pick the first parent branch of the this PR on top of the older branch:
```
$ git cherry-pick -m1 82f9a0eaa6b7bdf841ace05f5a23f0e54b63dd32
```

3. You will likely have some merge/cherry-pick conflict here, fix them and commit:

```
$ git commit -am 'Backport PR #35777: BUG: DataFrame.apply with result_type=reduce incorrect index'
```

4. Push to a named branch :

```
git push YOURFORK 1.1.x:auto-backport-of-pr-35777-on-1.1.x
```

5. Create a PR against branch 1.1.x, I would have named this PR:

> "Backport PR #35777 on branch 1.1.x"

And apply the correct labels and milestones.

Congratulation you did some good work ! Hopefully your backport PR will be tested by the continuous integration and merged soon!

If these instruction are inaccurate, feel free to [suggest an improvement](https://github.com/MeeseeksBox/MeeseeksDev).
                