BUG `DataFrameGroupBy.agg` with list not respecting `as_index=False`
- [x] Closes #52849(
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit)
- [x] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints)
- [x] Added an entry in the latest `doc/source/whatsnew/v2.1.0.rst` file

Dealing with non-categorical data is fairly easy, but dealing with categorical data is kind of tricky. I'm currently taking a pretty dirty approach, so if maintainers have better solutions please let me know and I'll make changes correspondingly.
@rhshadrach Thanks for your review! New test added and I've made your suggested modification. Thanks @Charlie-XIAO 