DEPR: Deprecate dtype inference on pandas objects
- [ ] closes #56012 (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.

This is very weird to begin with and becomes a real PITA when we infer strings as arrow backed strings
There was some weird additional inference going on in cat, which was uncovered by the deprecation, is fixed now but doesn't really need a whatsnew since we merged another fix today as well cc @mroeschke 

good to merge here? Should this affect pd.array? > Should this affect pd.array?

Yes, but it already preserves the dtype, so we should be good there