There are a few mixed feels on this for me.
If you think about being a one year old, one year seems a very long time to you. But once you hit your thirties years roll over like weeks and months. The longer you've lived the shorter a year seems. By 1 billion years old it may well seem that early centuries are like the vague memories of our infanthood. We'll view it as not fully developed, building the foundations to become fully developed people in whatever form that takes. Mortality will probably be viewed like we view sudden infant death syndrome.
But I think it's just as Likely that we'll have gone through several synthetic reincarnations, lifetimes stored on record but we are new people every several hundred years or so. Bodies and minds being altered and built in different ways but the core, the pilot of it all will be us still.
and maybe the boundries between us as individuals and maybe even the surrounding evironment will meld. We may still exist but in about the same way a cell exists in us. There may be this giant life form whose cells are the seething mass of humanity, it's thought the thoughts of a hive mind with it's own identity far more complex than the head of a single human could ever contain.
or we may be timeless entities by that point. where time doesn't flow in a linear route, and niether the multiverse or layers of dimensions bind us.
or we may never find the means to break the mortal binding. We may fix the diseases that kill the old now and be able to upgrade our bodies, but eventually the fragile web of brain matter will reach a limit that it cannot surpass and which tech can't bridge. and we will suffer collapse like house of cards, or begin fading away, forgetting who we were. Or even hitting a point where on more though, one more memory would so fundamentally change our brains that we would be snuffed out and something else would come to reside in our body.
Hell yes, especially the timeless entity part. And the seething massive hive mind part, that will be some real shit by then, not just communications--we're talking billions of years here, don't forget. But especially the timeless entity part.
This whole accelerating tech thing is just the latest episode in the universe show. It's a continuation of biological evolution, chemical evolution, physical evolution... the exponential acceleration observed in the tech of the 20th century - present has been going on since the beginning of the universe. And we assume it will stop because we can't imagine what that exponential curve looks like after the singularity. The singularity is not the end! The limits are extreme, and the limits are where we are headed. And at the bottom, at the quantum level, time starts to get weird. Therefore, WE will get weird.