Quantum immortality is not fundamentally about quantum mechanics. It is about whether you can live forever by defining yourself as a person who doesn't die. "You" can, but you can't.

That is just not correct, it is about how under some definitions of 'you', you don't die, and some people use those definitions regardless of QM (pattern identity theory uses a definition compatible with quantum immortality for example).

The real issue with quantum immortality is whether measure matters, and as far as I know, this is an open question (although, I suspect there are plenty of good resources on the question which I haven't seen)