As for Braxiatel and Iris Wildthyme's appearances in both continuities? Well, their timelines were always delightfully convoluted anyway. Iris has always been heavily hinted to come from another universe (The Obverse, not the alt-Whoniverse I'm now proposing).
Any continuity errors involving Iris Wildthyme are a feature, not a bug!
But it does change what we know about the history of the Time Lords, Rassilon and Omega's contributions, where regeneration comes from (prolonged exposure to the Time Vortex), and supplants the Doctor's origins on the planet to being of an unknown race and species.
I don't know that it retcons anything regarding Rassilon or Omega. They were the ones who invented time travel, whereas the Timeless Child only deals with regeneration.
But it doesn't jive very well with some of what has been implied about regeneration, which did seem to be a side-effect of their time travel. Some of the Season 6 episodes like "Day of the Moon," "A Good Man Goes to War," & "Let's Kill Hitler" established that Melody Pond had regeneration abilities because she was conceived on the TARDIS while it was in flight.
What he does with this in moving forward - since there aren't many more shocking developments he can use to throw off clunky dialogue arcs and passive style... - especially as the consolidated figure revealed yet another 300k VANISHED due to youtube clips of the episode from official sources combined with news articles shows Chibnall's heading down the wrong path or took the wrong approach. Even if the AI went up one point. They have fewer viewers but those that remained are hugging it.
Wasn't that basically what happened to the show back in the 1980s? They kept shedding viewers each season while the AI scores kept going up accordingly. What happens is that the show loses casual viewers and all that's left are the die hards.
The point of the Timeless Child origin for the Doctor isn't that they're perpetually immortal; the point is that they were lied to, abused, and enslaved over and over for centuries.
Yes, but for what narrative purpose? What does that have to do with a plot by the Master to create an immortal army of Cyber-Time Lords?
The thing is, I don't object to the lore changes in principle as long as they're in service to the story. I actually really liked the main Cybermen/Master story of the last 2 episodes. It felt much more
Doctor Who-y than most of the Whittaker episodes that I've seen so far. But taking the Doctor out of the main story so that the Matrix could give her a big info-dump served no purpose. Maybe there will be a later episode that will pay off this Timeless Child stuff in such a way that it will all be worth it but I doubt that Chibnall has that kind of talent in him.
Also, what was the point of Jack's warning back in "Fugitive of the Judoon"? He told the Doctor not to give the Lone Cyberman what he wants. But she did anyway and everything seemed to turn out fine. Heck, what was the point of Jack appearing in "Fugitive of the Judoon" at all apart from (1) continuity porn and (2) keeping the companions out of the main story because Chibnall can't figure out what to do with them half the time, same as in "Spyfall, Part 2."