TL;DR — adding P_CURSOR_EDIT to Transform_Properties in TRANSFORM_OT_rotate streamlines cursor manipulation.
At the moment, in order to rotate the 3d cursor via hotkey (without addons), you have to call transform.translate and then hit R to swap from translation to rotation within the modal. It’s a useful behavior, but it doesn’t feel like an intentional one. All of the relevant features are there, but they aren’t put together in a way that’s accessible for users.
Making the property more accessible is an easy one-line tweak that I’ve managed to bumble my way through in an afternoon. I haven’t encountered any unexpected complications from it in my local build, and it opens the door to some fun stuff for addon developers.