Lol space will NOT make any difference at all. That technology is not progressing at a rate where we could have millions, let alone billions of people inhabiting space in the near future. We’d also pretty much be completely limited to our solar system, meaning planet-wise we have maybe Mars and Europa and Titan at best… but there’s absolutely no chance of any meaningful colonial activity on those planets, Mars would probably have something similar to Antarctic research facilities on it but that’s about it.
Near enough to be relatively confident in how much we won’t progress in terms of colonizing space. The general public severely underestimates the limits to space travel & survival. It’s not like I can tell you exactly what or when technology will be like in some exact point in the future, but it’d probably be a few hundred years until we could actually make nation-sized space colonies, and there’s pretty much no future where space habitation replaces or becomes greater than Earth habitation, unless we go ahead thousands if years. There were a few interesting astrophysics papers estimating that near-lightspeed and FTL travel tech is like 8000 years away lol.
“Future technology” can’t solve all of our problems. It’s not magic.