If you keep the original bioware fully operational, it's more like an incremental fork running on an emulator. You can start having conversations with your approximated self.

The Ship of Theseus is a weird one too. If you take a car apart and replace it piece by piece and replace the whole car you kind of have the same car. But what if you kept all the old pieces and put them back together? Which one is the original car? It is a interesting thought sub experiment that plays on the 'Ship of Theseus'. You could end up with the same issue here. If I make a perfect copy of myself, who is the 'real' me? There is an obvious 'older' me but the other one is just as capable as I am.