REF/BUG: DTA/TDA/PA comparison ops inconsistencies
It will take a couple of steps to get these three methods to all behave the same.  Following that we can move to share code between them.

This came up when trying to make the indexes dispatch `searchsorted` and it turns out that the DTI/TDI/PI searchsorted methods are not consistent with their DTA/TDA/PA counterparts.  The fix is to have shared validation/casting methods, which should in turn be consistent with the comparison ops.
Thanks @jbrockmendel