REF: Refactor GroupBy a tiny bit
- [NA, small] closes #xxxx (Replace xxxx with the Github issue number)
- [waiting for review] [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
- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [waiting for review] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

@jbrockmendel how about I drop the commit where I add `dropna`, address the other tweaks you suggest, and then we can merge this as a start? And then maybe do those offshoot changes separately? This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. Looks like this is a bit more than I want to take on, but I pulled the less-controversial changes into https://github.com/pandas-dev/pandas/pull/46754, where hopefully they can still be merged.