Personally, I think that if humanity progresses that far technologically, without destroying itself, we probably won't care that much about habitable planets or planets with water. We'll just live in space and harvest the energy and resources that are available nearby. There are a lot of other planets much closer to us than K2-18b. We could just build bases in orbit around those stars, harvest asteroids for minerals and hydrogen for fusion power.
Alpha Centauri would "only" take 22 years to reach at 0.2c (plus some time for acceleration and deceleration). You could leave earth and live to see that solar system, and you could travel there on a ship that is basically a large city that will just park itself in orbit around the star on arrival, acquire resources, and start building something bigger.
This will make the 22 year trip to Alpha Centauri more palatable.
1000 year trip in a single lifetime will require some life extension as well
Perhaps not ships containing humans, but some kind of other tiny ship containing a replicator machine and DNA for humans.
For 0.999c, it would only take around 71 days to reach Alpha Centauri from Earth (as seen from the ship). That's pretty mind boggling.