I'm a little bit worried about all of human civilization.
I've put a little bit of thought into where this might come from. It's clearly not a realistic thought. There is no meaningful way it impacts your life. Both evolution and technology progress on vastly faster time scales, and so there is nothing for you to gain from thinking about it now.
Pop psychology suggests that it's perhaps depression or boredom. They're catastrophizing to avoid thinking about something else.
If it's causing you distress, you could consider seeing a therapist to get to the root of the problem (which almost certainly has nothing to do with the sun). If it's merely a way for you to amuse yourself and isn't making you unhappy, it's no worse a hobby than a lot of others I can think of.
Maybe there is a big meteor that resets everything, already hat that once :D. The sun burning out is so far off, my grand, grand, grand, grand, grand, ..., grand kids are still fine in that aspect.
The event you're worried about is so far out in the future that no discussion about humans, or any living organism for that matter, is meaningless.
Regarding time scale, 15 thousands of years ago there was no civilization, 100 thousands of years ago there were not even language, a couple of millions of years ago there were not even hominids. In that context 5 billion years (or just one, as when the sun starts to get into red giant phase life won't be possible here) is just meaningless.
In the other direction, change in our civilization is accelerating, how we went from knowing barely the continents were in, to finally have a global understanding of how it was the world, then global communications, fast travel, globalization, internet and AIs were things that happened increasingly faster. If we don't crash soon somehow. we might be able to at the very least to make self-sufficient space environments within this millennium and not be tied to a single planet.
I try hard not to worry about the things I cannot change.
As far as the sun dying out though, I reckon the human race (or its distant descendants) has enough time to deal with that. I'm more worried we will kill ourselves off long before that becomes a problem.
Your species’ current definition of “civilization” isn’t going to make it anywhere near 600K more years, though I think you probably missed at least an order of magnitude anyway.
It’s not going to stimulate much in depth conversation other than the usual ‘humans won’t be around by then’ response.
But I am disappointed that if we screw up badly enough, any subsequent species rising to our level probably won't have the time or resources left to go on and surpass us.
Sorry, perhaps took your remark out of context, but the fact remains.