If that is immortality then we may as well call it a tautology and say we're already immortal. None of the things that make people who they are need to be preserved to achieve it so we're realistically already there.
Living an absurdly long time I can get behind. Billions of years, trillions of years, unimaginable numbers of years, sure. That could happen. But immortality isn't an option, everything eventually dies off unless we play semantic games where there aren't any properties of the thing that need to be preserved. And maybe even reality has an expiration date for all we know, which would render the whole project moot.
For some people, the idea that their present conscious moment might eventually be left permanently without any future extension is terrifying-but provided that doesn’t happen, they might be neutral (or even positive) about the prospect of the contents of that consciousness eventually becoming so radically transformed that it becomes a completely different person, or even something which transcends human notions of personhood, albeit ultimately still continuous with the person they are now. For other people, that prospect is terrifying. It really depends on what one is most attached to - the mere continuation of one’s own consciousness, or its distinctive contents that makes you you.
