ENH: partial string indexing on non-monotonic PeriodIndex
Looks like the DatetimeIndex analogue of this was done in #2437 (https://github.com/pandas-dev/pandas/commit/3a173f19b308d2fb7d8e96dfc57f2e5ecd046138)

This does _not_ yet support two-sides slicing e.g. `ser["2015":"2016"]`, but im hoping to get that handled before long.

Partial overlap with #31058, nothing should actually conflict.
Is this a bug fix or a new feature? Can you add a whatsnew? > Is this a bug fix or a new feature? Can you add a whatsnew?

I think it counts as a feature, but there are a lot of inconsistencies in the surrounding code, so I wouldn't argue the point.  Just added whatsnew. can you rebase one more rebase rebased+green Thanks @jbrockmendel 