Where I am, we don't have the "do not cross solid white, double white/yellow" thing for our carpool lanes. (Kinda sucks actually, since people enter/exit willy nilly)... But anyways, the car seems to be programmed to think that you cannot cross a solid white, so it's a pain in the ass, because AP/FSD will refuse to change lanes across it. If you forget to drop out of AP/FSD and try to go across while signaling, it will try to force you back into the carpool lane.
By the way, on mine I noticed when I use some of the flyover carpool lanes and/or interchanges, it switches visualizations to the city streets mind of car view, even tho I'm still on the freeway. Sometimes I wonder if the switching stacks from freeway/city causes some of these issues with the lanes thing you mentioned.