Verbeena, asking these questions about definitions and meanings is not a point scoring exercise. It's not a game. It's not a bit of intellectual masturbation.
It has real life consequences. If your defining factor is a sense of self, that is something that no one can observe or verify. If you claim that transwomen have it, there must be some way of identifying it. Otherwise self ID is exactly what you are agreeing with.
How can women organise, or uphold their rights, if they are categorised by something entirely subjective and which doesn't hold up, in any material way?
Genuine transsexuals very rarely say they have a sense of self that means they are female. They will talk, at length, about how they reject their masculinity. About how presenting is female alleviates their symptoms.
Historically, they had to understand that they were indeed male, before any medical intervention was approved. Because otherwise it's just a delusion.
You saying that the defining factor in the concept of a woman is a sense of self, is directly undermining the reason why women have their own rights. The inherent power dynamic between men and women is dictated by biology and socialisation. Not a sense of self.