CLN: Refactor groupby._make_wrapper
- [x] closes #48028 (Replace xxxx with the Github issue number)
- [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) to new arguments/methods/functions.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Currently keeping the docs the same, plan to make groupby-specific docstrings in the future. Note that most of the SeriesGroupBy docs don't make it into the documentation, I've opened #48399. The only change from a user-perspective here should be that Jupyter / IDEs can now get the correct signature (instead of `*args, **kwargs`).

![image](https://user-images.githubusercontent.com/45562402/188480390-ec9f26c3-ec3d-456d-961b-1843713b8679.png)

![image](https://user-images.githubusercontent.com/45562402/188480951-4e679091-0c7a-402b-8c9e-7e8293f793d1.png)


Awesome! A lot more straightforward, thanks @rhshadrach 