BUG: Fix all-NaT when ArrowEA.astype to categorical
- [x] closes #62051 (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).
- [ ] ~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.

Using `astype` with `CategoricalDtype` coerces values into `Index`, where the code tries to compare two `Index` objects with numpy and pyarrow types. 

In the first example, the code does not think they are comparable in `Index._should_compare`, and returns all -1s. In the second example, the code correctly determines that they are comparable, but they try to compare it (coercing both indexes to object dtypes with `Index._find_common_type_compat`) and fail. Hence, both cases return all -1s.  So we should start by fixing should_compare? > So we should start by fixing should_compare?

Sorry I missed this earlier. The fix I pushed addresses that and resolves the second issue too. 