Way before that the carbon cycle will stop and most life on Earth will starve. Yet way before that we'd have evolved into different species that will likely go

Way before that the carbon cycle will stop and most life on Earth will starve. Yet way before that we'd have evolved into different species that will likely go extinct as they all do (I think the average lifetime is 10My). I don't know where this idea that we might still be here until the death of the Sun came from. I'd worry more about making it to the next glaciation without having poisoned ourselves before. I don't think it's accurate thinking about space as a physical place out there you can simply go. It's more like jumping from one gravity well to another and what you have to think about is what part of the system you're aboard can do that by means of conservation of momentum. And that's the main reason why I don't think we have the technology nor the energy budget to think about feasible interstellar trips. It's a bit like telling techno fairy tales to children, only it's adults and we have a lot of other adult problems.