Must a woman who scratched her vulva in Ramadan, accompanied by the discharge of secretions she doesn't know are manī or not, due to vulvar itching for which ointments were ineffective, make up that day?

You are not required to make up for the fast, because the discharge from the vagina does not invalidate the fast according to the consensus of scholars. Even if it is accompanied by some pleasure, it appears to be natural discharge, for which only ablution is necessary, along with washing it and whatever it has touched on the body and clothes. The default is the validity of the fast and that semen has not been discharged unless there is certainty to the contrary.