From where I’m sitting, it looks like death should not be the end in that case.
You can’t perceive the passage of time when you are dead, so you’re just going to experience dying and then immediate rebirth after the countless eons pass for that rare moment where entropy spontaneously reverses to form your mind again.
I don’t think given an infinite amount of time the universe would produce an identical me. That’s such a specific combination of matter and chemical processes it just feels silly to assume it would happen. Even if I agreed that it would inevitably happen, I think there’s an implication that a very large number of almost but not quite mes would also come into existence (because if I understand the premise, it’s basically “on a long enough timescale every possible thing will happen”) and frankly that’s more disturbing than ceasing to exist (which, to be clear, is very disturbing to me).
I’ll also say that a clone of me with my memories is still not me. Such a thing could exist simultaneously with me and it wouldn’t reduce my desire to personally remain alive even slightly, it’s a different guy, but with a lot in common with me.