Interesting thought experiment, but I would be careful with the phrase “immortality”.
Survival of information, continuity of observation, and survival of a person are not the same thing.
Even if reality is understood through branching, information, or observer-relative continuity, the hard question remains:
what exactly continues?
A body?
A memory pattern?
A causal trace?
A subjective stream?
A reconstructed identity?
Death is also not one simple category. It depends on what system is trying to end, what continuity is being tested, and what kind of information remains bound to reality.
So for me, the deeper question is not “do we simply never die?”
It is:
under what conditions can continuity survive without becoming only a copy, echo, or external trace?