Revert "BUG: Timestamp origin takes no effect in resample for 'MS' frequency (#53938)"
closes #55064

This reverts commit dfc4c3900a181e8a9dff724217d5a14e59ca2e4f.

- [ ] closes #xxxx (Replace xxxx with the GitHub issue number)
- [ ] [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).
- [ ] 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.

---

I'm just:
- reverting the commit
- fixing some merge conflicts due to:
  - random number generator usage
  - 'T' -> 'min' deprecation
- adding a docs note noting that `origin` only takes effect for tick-frequencies

and adding a 2.1.1 whatsnew note
Thanks @MarcoGorelli 