Similarly stomach is sometimes used to cover basically anywhere in the torso from the lungs down.
I've been thrown by this before, and it's even worse when a professional uses "tummy" to refer to pretty much everything on the front and sides from the bottom of the ribcage down to the hips. I think they're trying to put people at ease doing that but I always find it off-putting and confusing because to me that sounds like something stomach or at least digestion-specific rather than the rest of what can go on in that area.
I don't tend to talk about genitals much in person, certainly never discussed a bikini wax and typically when discussing medical things, the specific part is left off as with issue with things llike UTI or tears during birth, I wouldn't think of going into the specifics with almost anyone outside of a medical professional.
I've used vulva when talking to my kids, I've also used genitals, bits, 'what's in your pants' (typically involving asking them not to play with them in public), and probably a bunch of other things. I agree that mocking or correcting someone for using any term when you know what they mean is pretty rude, but I don't get why using specific terms is more sanctimonious unless they're correcting people on it. I knew some very sanctimonious growing up who called it all 'hoo-hoos' and had rather low opinions on people using specific terms. I think there is space for both being precise and general social terms that we don't need to divide people into groups for which they tend to use.
Only on here do I see people use foof, front bottom, cookie, I've heard fanny on TV a few times but I can't recall anyone actually saying it in person around me and typically on TV it involves jokes about the difference in the US and UK usage. Maybe I just have a social circle that doesn't discuss their genitals much.