On one hand, I agree that tpotd wasn't Really a Thirteenth Doctor episode for a variety of reasons, it's just only some of the reasons annoy me.
I'm annoyed that she left on a gimmick episode, because it wasn't about her doctor, and while i actively appreciate her era for sharing the title of doctor with other women (Jo Martin as Fugitive and Yaz), there's a very fine difference between sharing and toe stomping over somebody else's parade and while i'm not inclined to place any fault at the feet of the actors of the classic doctors in the episode (it was, after all, an anniversary celebration of sorts and their presence makes sense) it Does irk. I mostly blame the plague and the absolute Nightmare the beeb made of this situation for this, it could have been handled infinitely better in so many ways.
But also, there're some reasons that it gets called not a Thirteen episode that I don't Really agree with in a textual sense. Thirteen's arc in that episode is so deeply personal and affirming to her journey. What it Isn't is flashy. But that's kind of by design in my opinion, because while we often take note that Yaz is the Doctor in this episode, we don't often acknowledge that the doctor is off doing something more companion-y that is deeply personal to her storyline.
Yaz starts the series begging her boss to do more, be more, Help more. She wants to help people and and first she started doing what the woman who helped her did and it wasn't what she thought it'd be. Then Thirteen comes along and suddenly she has the power to move mountains and help so many more people than she'd ever considered. Her arc's culmination was becoming the doctor and doing that, having to save the world because she's the one who was there to do it. Doctor Yaz is in the house.
Meanwhile, Thirteen's arc is not about saving others, it's a metaphorical saving of herself. When she finds out about the timeless child, but before she finds out that She's the child, she asks, horrified, what happened to the child? Did anybody help the child? Because she knew what she was being shown was a horror story.
She then finds out that that kid was her, and no, nobody did save her. They did get free eventually, so it's not a wholly sad story. But nobody intervened and helped that child.
So when a being appears that the master is using to power his schemes, a being that appears as the thing the viewer will most likely protect, it takes the form of a little black girl. Like the original timeless child who nobody ever helped or took care of properly.
13's desire to have been cared and loved and protected in physical form placed in front of her face.
Thirteen saves this little girl. That is her victory. It's her moment. The metaphorical saving of self, the love and care she never got given to another. An apology given (even though the doctor was guilty of nothing) and a rescue and freedom. Liberation.
In short, Yaz's arc was about getting bigger, helping on a wider scale, saving the world, being the doctor. Thirteen's was about the individual, it was personal, it was inherently about breaking a vey personal cycle of abuse and saving the little girl she used to be. All this after Tecteun accused the doctor of being just like her. But the doctor is nothing like Tecteun and never has been.
It's an inherently companion style hero moment, is it not? Is it not like Donna insisting they at least save Somebody in Pompeii? Just because it's important? That one person is important.
So I guess, while i do resent the furore around a bbc anniversary taking away 13's thunder. I do not resent the fact that 13 and Yaz's arcs were always about them turning into each other and them Both still being heroes, because saving a tiny vulnerable girl who's being victimised is as important as saving the world. That episode was as much about 13's culmination as it was Yaz's, it's just they were just swapping who did what.
