We could go live nestled up close to a red dwarf that has tens of billions of years of life left. We could dyson sphere it.
I'm using "could" very loosely here.
Indeed - a lot of things are theoretically possible, but most things out there are things that people assume we'll eventually be able to do, or if they say "We technically already know how to do this." its something that works out mathematically if you had infinite funds and infinite energy and the attempt when flawlessly with no hiccups.
I think we vastly overestimate our future technology potential, and assume infinite linear progression forward for all technical capabilities. Realistically there have been and will be many plateaus in technological advancement, and there will be many things we eventually just hit a limit imposed by the laws of physics.
I think in all likelihood our species will eventually go extinct here on this same planet. I don't really think we'll ever be able to reach another star. We might attempt it with an AI probe (since they can technically live "forever") but I don't have confidence in us being able to build anything that will last long enough to reach another star system. Even a robot/computer would likely just be a non-functional piece of equipment by the time it arrived.
Its not an exact analogy but think about an iPhone or desktop computer and how much worse they work after they're 5 or 6 years old. Now imagine one that's 50,000 years old . . .