Minor quibble. That is the distance to Promixa Centauri. To my knowledge, we don't know if there are habitable planets there. Proxima B is within the "goldilocks" zone, I believe. But we haven't had any measurements consistent with an oxygen atmosphere (and it would be foolish to send people there without confirming they could at least breathe).

It's super unlikely we would ever find an earth-like planet that's close enough to be reachable with less than faster-than-light transportation and have an oxygen atmosphere. I think any discussion of extraplanetary colonization has to start from the premise that there won't be a breathable atmosphere.

The huge advantage of Proxima B is that it's estimated to have a mass of about 1.07 Earth, which means it solves the one biological problem that can't be solved by any technology we have today - gravity. Many of the hazards to human life in space are environmental dangers like radiation, extreme temperatures, lack of breathable atmosphere. But those can mostly be solved by building a habitat underground, which shields against most of that. But the one thing you can't solve for is low gravity, like you would have on the Moon or Mars. Our entire physiology is based around the presence of Earth-normal gravity, and it takes a ton of very intentional and specific exercise by adult astronauts to keep their bodies from falling apart in zero-G. It's hard to imagine what would happen to a baby growing up in a low-G environment.

That's probably the biggest barrier to near-term space colonization: it's probably impossible for babies to grow to maturity in a healthy way anywhere that isn't close to Earth-normal gravity.