Backport PR #51643 on branch 2.0.x (API: ArrowExtensionArray._cmp_method to return pyarrow.bool_ type)
#51643

- [x] closes #51980
@lukemanley could you take a look at the doctest failures? Is this expected to fail? > @lukemanley could you take a look at the doctest failures? Is this expected to fail?

looks like you already identified #51631 needs to be back-ported first Yep, thx