test backportability of #38120
#38120
@jbrockmendel the test faiures are for PeriodArray/Index. There must be some differences on master on how this is handled. will continue to investigate. so it appears the class hierarchy has changed.

I think the docstring for DatelikeOps, 'Common ops for DatetimeIndex/PeriodIndex, but not TimedeltaIndex.' and TimelikeOps is now confusing.

I'm not sure why the merge put the new implementation of factorize in `DatetimeLikeArrayMixin` instead of `TimelikeOps`, but if it's put in `TimelikeOps` then the base EA implementation of factorize will be higher in the MRO.

so have kept it in `DatetimeLikeArrayMixin` and overridden in `PeriodArray`