POC: _eadata
With _index_data figured out, it is now feasible to implement the DTA/TDA inheritance->composition changeover independently of all of the rest of #24024.  This PR is a proof of concept for what that would look like.  The steps would be roughly:

1) Instead of dispatching to `self._data`, we temporarily implement `_eadata` and dispatch to that
2) Stop mixing DatetimeLikeArrayMixin into DatetimeIndexOpsMixin
3) Stop mixing TimedeltaArrayMixin into TimedeltaIndex
4) Stop mixing DatetimeArrayMixin into DatetimeIndex

For demonstration purposes this PR implements step 1.  I have local (test-passing) branches for each of the other steps.