This is my take as well. Once you’re the 3ER, with all of time constantly populating your mind, the short timeframe of Brandon Stark is irrelevant. He no longer has any concept of nor loyalty to being a Stark. Brandon Stark is effectively dead. We have now the 3ER.
This was a literal conversation between Bran and Meera. Bran said he remembers what it was like to be Brandon Stark but he also remembers much more. Meera responds by saying he died in the cave
I don't even think he's human anymore. Look at the way he said goodbye to Meera or greeted Arya. He's just a 3ER, not even a human.
I just hope D&D don't botch it up this time and essentially try to pull a cop-out where the 3ER still has some sentiment/loyalty to the Starks. I'd much rather prefer one or the other but as it seems with how s7 left off, I don't think D&D are going to write him to be disloyal (or at least uninterested in the Stark goals).
Plus he's gonna be essentially 100+ by the time he does die. Last one was old as fuck.
Bran is going to survive, crawl back beyond the remains of the wall, hook himself into the Weirwood Net and wait to train the next 3ER in a few thousand years when this inevitably happens again.
Wights
marching