ENH: Better dtype inference for reductions on dataframes
- [x] closes #40669 (and probably others, I will check later)
- [ ] [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.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

I think the code itself is ready for review, but this needs more tests, and just checking now if the CI raises anything unexpected.
xref #52261 Superceeded by https://github.com/pandas-dev/pandas/pull/52788, closing.