I don’t agree with any of what you conjecture. Assume you have much better technology as ours but we roughly correct in our current understandings of physics and energy. So let’s try building space habitats with square foot like our planet’s surface that can accommodate exponential growth in demand, really? Before you say well they will have a different habitat, that’s easy, we can even almost solve that, little DNA programming we can likely adjust our DNA to incorporate features that make earth’s atmosphere habital. Now the “incredible” resources to get here. It’s nonsense, the first arrivals will be automated probes, lightweight. Again we can almost easily do this and we just got started.
Lastly, the idea we aren’t looking for habitable planets with in the back of our minds colonies is silly, of course we actually are, we can make all the excuses we want to try and justify our real intentions.
We are on exactly the path I suggest they are likely on. Find planets, send probes, sample lifeforms if found. Send seeds. It’s the universal life force that makes us do it. It’s what life does, expand, replicate, grow, spread.