BUG: Add PyArrow datelike type support for `map()`
- [x] closes #61231 (Replace xxxx with the GitHub issue number)
- [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
- [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.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Can you add tests based on the original issue Looks like some tests are failing in the CI.  Can you address those? @jbrockmendel sorry I was inactive last 2 weeks. Will take a look at this issue atm I now used `self.dtype.kind in "mM"` instead. 

I saw that the test function (`test_map()`) uses it to test out datetime likes. So I realized its best to use it to filter out datetime likes on the function as well @jbrockmendel Is the fix for the existing test_map enough? or should I add a test similar to the issue as well? Thanks! Can you add a test associated with the original issue.  it isn't clear from the edited test that it is fixed