BUG: Fix concat dtype preservation through concat
- [x] closes #51362
- [x] [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.


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Expected behavior:

- An empty categorical, and a categorical should concat as a categorical.


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Linked issues:
#13524 see https://github.com/pandas-dev/pandas/issues/13524#issuecomment-233792648
https://github.com/pandas-dev/pandas/issues/39443

#14177 (seems a dev call agreed on putting this as an option in `concat`)

https://github.com/pandas-dev/pandas/pull/13767


As mentioned in #51362, this is not a bug, but we are willing to support this via a keyword in pd.concat.

I think there are also some older related issues this would close.  Can you make sure those are listed in the OP. Closing this for now — I ran into more complexity than expected. Might revisit later with a cleaner approach.