alright I did too much thinking. So. The Doctor's regens are somewhat influenced by his companions, right? We see this most prominently with 12, whose face was a promise to both himself and Clara. Now, who were 12's more prominent companions? Clara and Bill. His Impossible girl and his student. What does 12 regenerate into? A woman. Clara tried breaking down 12's walls, and semi succeeded. 13? amended that, and tried to be more open with the Fam. 13's base idea is all Clara- a last promise to her Impossible Girl that she'll get something right.
13's personality though. The excitedness, the attempt at being casual? The bright clothing compared to the usual black and blues, the chattiness unlike 12? That's Bill Potts, through and through. The Doctor still doesn't know she was alive, that Heather saved her, and it was one of his biggest regrets, and it's a silent apology to her student. A silent I'm sorry. (also both of them were gay and fall for people with the opposite hair color- light vs dark)
