ENH: Experimental Higher Order Methods API
Start of #41112, second attempt at #43736.

- [x] tests added / passed
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit) for how to run them

Built docs can be viewed in #43736 (wording slightly changed from there, but results are the same). If we go forward with this approach, needs to run on the CI with failures allowed.

cc @jbrockmendel 
Might wait until Monday to take a look.  Troubleshooting azure left me cranky. @jreback @jbrockmendel friendly ping.