Fixes NonExistentTimeError when resampling weekly 
- [ ] closes #53666 
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) 
- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).

@MarcoGorelli thanks for reviewing.
Do you have any recommended steps to get started?
 @mroeschke Please could you help my mentee with advice/review here? Thanks Sorry for the delay here. I don't think anyone on the core team has bandwidth right now to suggest a quick solution to this complex issue right now. As alluded to in https://github.com/pandas-dev/pandas/pull/54609#pullrequestreview-1583975480, this may require a larger refactor.

Going to close for now, but happy to have contribution on other issues