Call me a pessimist, but I would be extremely surprised if humans are still around then.
Why is that? Despite what pessimists - and even the occasional realist - have been saying for decades now, so far humanity has avoided extinction or civilization collapse. Even the arguably most urgent as well as most important problem for decades to come (climate change) isn't an extinction-level event, even in a worst-case scenario.
So far, mankind's continued existence depended on a rather fragile foundation. Once mankind develops into a multi-planetary species, which we are on the verge of becoming, simply all bets are off and things might work out either way.
Becoming a multi-planetary species might be the Great Filter we seem to be observing. Paradoxically, that we have yet to meet any species that has already passed that filter, makes it more likely for humans to simply be the first ones to do so.
Just alone the fact that people cannot even speak freely without censorship and of certain topics in order to discuss objectively whether they are legitimate or possibly a greater risk than climate change, specifically because the conversation and topics themselves are forced and enforced, is also a very good indicator that things will not go as well as people want to tell themselves.
You say we are on the cusp of interplanetary existence? Just alone the realities of that state are likely to cause more problems that could lead to extinction than not. For example, it is far more likely that humans will rather rapidly diverge in evolution between planets for several reasons, which can lead to all kinds of issues not directly related to whether one of the species of human will survive.
We are in a global toxic relationship with each other and are not even clear about fundamental questions of agreeing on basic facts or being able to even just examine whether all the basic assumptions are correct. How one could expect that to allow us to face of extinction is beyond me. However, it strikes me that lying to oneself of faking it til you make it will simply not impress a cold and calculated mistress as reality.
Fair enough, though. It perhaps is true that climate change is assigned undue importance in public discourse when compared with other problems that might be just as important - or even more so.
You'd be hard pressed, however, to find an issue that has as many immediate (or near-future) and potentially severe repercussions for as many people.
Evolutionary divergence certainly seems like a potentially relevant future problem, the key word here being "potentially", though. Climate change, on the other hand, is a certain reality. Assigning the same resources to both problems, even though one of them might never even materialize (or do so in a manner we can't even anticipate yet), therefore would be irrational.
That doesn't mean, however, that we can't work on solving both at the same time. At the very least, 8 billion or so people allow for massive parallelism.
Arguable indeed.
There is un circumstance: that a group of humans today (or in the near future) just time "travels in the future" (e.g. by moving at relativistic speeds, etc, while in cryogenic sleep or whatever) and just happen to witness the late universe without the time actually ticking for them. In that (unlikely) case the same effect that would prevent the species from diverging is the same that would prevent them from getting extinct (not enough time)
There’s an interesting way to get to relativistic speeds - to get close enough to a supermassive black hole, steal enough momentum so you get very close to c, then, a subjective week later, you do the same around another black hole in a different galactic core to shed your momentum and get back to a manageable speed. An intergalactic civilisation would use supermassive black holes as train stations.
Once you have that you inevitably have groups heading off into space in different directions, never to return to Earth, but some will survive trips to other stars, and some will multiply and branch out from then
At that point humanity or its descendants will inevitably fill the entire galaxy, although it won’t be a single civilisation.
Today if you took the scrapable internet + wikipedia + all academic journals, you still probably lack enough detail and method to reproduce techniques in manufacturing, mining, tooling, medicine, and so on.
If the hypothesis is that humans will survive so long as we are off-planet, then the humans leaving the planet need to be able to do everything fully disconnected from the home world to really survive if something happens to the populace on the home world.