Is ghusl obligatory for a Thayyib if semen reaches the outer vulva, and for a virgin if semen exits the vulva completely? And does this apply to all vaginal discharges of a girl and a woman?

What was mentioned by Al-Nawawi is correct regarding what exits from a woman's private parts. If she is a virgin, what is considered is the protrusion of the discharge to outside the vulva. As for a non-virgin, what is considered is its protrusion to the place she is required to wash during ghusl (definition) and istinja (definition)' (ablution for relieving oneself), which is what becomes visible when she squats for her needs. The difference between them is that the inside of a virgin's vulva is considered an inner part, so she is not required to perform ghusl until semen exits from it. As for a non-virgin, she is required to perform ghusl if semen reaches the inside of her vulva, because it is considered an outer part.