WIP: Dispatch Series comparison methods to Index implementations
Same thing we've been doing for arithmetic operations, now moving on to comparison methods.  Based on some trial-and-error, it seems like there are some inconsistencies to be worked out for the categorical dtype case.  This PR:

- Dispatches timedelta and datetime `Series` comparisons to their respective `Index` subclass implementations
   - Patches `DatetimeIndex._assert_tz_awareness_compat`, which has already been broken out into #19276.
   - Kludges `datetime.date` and `None` case that `Series` treats differently from `DatetimeIndex`; decisions should be made about those so these kludges can be removed.
- Removes a `# temp workaround until fixing GH 13637` for comparison with `PeriodIndex` that appears to no longer be needed.
- Fixes names of the results for comparisons between `Series` and `Index` classes. (probably needs tests)
- Notes some small inconsistencies in how `_constructor` is called, also discussed in #19271.