ENH/DEPR: infer date objects to date[pyarrow] dtype
Sits on top of #53025.

A few issues this brings up that we should decide on before merging

- [ ] constructing a Categorical from an object-dtype Index does type inference on the categories; is that always wanted?
- [ ] infer_dtype will see a mixed sequence of dates-and-datetimes and return "date"; sure we want that?  AFAICT the main place it is relevant is in Index._maybe_promote
- [ ] Desired behavior of `DatetimeIndex.get_indexer(index_of_dates)`?  ATM the index_of_dates would have object dtype and get cast to DTI in Index._maybe_promote.
- [ ] date32 vs date64?
- [ ] extend the relevant tests with the future behavior
- [x] handle construction from scalar
mothballing until after (at least) #53025