> I've lived longer than you have.
Let's not play that game. Neither of our relative ages matter for the purposes of extrapolating to billion-year lifespans, nor do they render you particularly qualified for deciding whether such people will get "bored". Far more qualified people than either of us have done research on the topic, and I have at the very least read many research papers and articles by those who do.
> No, it is your unbounded optimism which is unjustified, unless you can figure out how to do an end-run around relativity.
The sun burning out is a problem we can already hypothesize ways to solve now, given technologies whose development has a scale of "centuries" or "millennia" rather than "billions of years". The most obvious solutions involve leaving the planet, and that doesn't even touch on the possibilities of stellar engineering. That's easily imaginable within the scope of today's science fiction, let alone the unforeseen technology of even thousands of years from now. I feel quite safe making the prediction that, conditional on humanity lasting the billions of years between now and then, the sun's expansion will not destroy civilization, humanity, or any non-trivial number of lives.
Much more critical existential threats, likely to be a problem on much shorter timescales, include nearby celestial events, collisions, or other things we don't have billions of years' to prepare for.
As for longer-term problem of continued existence in the universe, I wouldn't hazard a concrete prediction, but I'm sure we'll learn a great deal more about physics between now and then, not to mention likely existing in a form where thought and subjective perception of time (as well as the ability to solve problems) can occur far faster than "one second per second". In any case, I think it is safe to predict that people will not actually give up on that problem until actual effort is put forth attempting to solve it for a very long period of time.
Besides, my optimism has come up against cynicism and fatalism far worse than yours and survived unscathed, and it continues to serve me well. I don't find that fatalism is conducive to actual solutions. (And when it comes to actual predictions, I aim for accuracy rather than either overestimation or underestimation, but I find that hope tends to help as long as it accompanies actual action.)
> First of all, I don't want to die. Dying sucks. But living forever would suck more.
That's a testable hypothesis. If it turns out to be possible, why not try it and find out, before deciding in advance how you'll feel countless years in the future? Not like you couldn't change your mind later if you still feel the same way.
> You really could experience every possible sensory input an arbitrary number of times, and eventually you would get sick and tired of everything.
There are entire branches of research dedicated to exploring and solving this problem. That research looks at concepts like what we actually find interesting and fun (for one example, problems that are difficult enough to be a challenge but not so difficult that we can't make progress or learn something), the classes of things we can find fun at different intelligence levels, and ways to ensure that the number of interesting things to experience grows faster than the amount of time available to experience them in. In short, no, you will not get bored.
(And that's not even getting into very dangerous failure modes like "oh, what if I just modify myself to not get bored", which is incredibly problematic but still a more interesting hypothetical attempt at actually trying to solve the problem rather than giving up.)
> That too. But it also needs you. And everyone else.
I already have a problem to dedicate my life to. Many others do not, and they would be better people to target with your advocacy. I would suggest that you'd do much better focusing on "this is an important problem to work on" rather than "drop this specific cause and work on this one". Fortunately, humanity is capable of doing more than one thing at once, and in fact should do more than one thing at once. These goals do not conflict with each other, and a much smaller set of people is able to work on one than the other, which strongly suggests a benefit to specialization.