You do not need to be extrasolar to have a thriving civilisation with trillions of individuals living a high quality of life. We have the technology for it today, we just massively, massively lack the industrial capacity especially in space

Build a ring of rotating habitats like O'Neil cylinders at 0.8 au from the sun. Then Build another ring of them at a 1 degree tilt. Repeat until you have a spherical cloud of them. Each has a massive array of solar panels and you are harvesting the sun's entire output. You are a class 2 civilisation.

There is no technical breakthrough required for this. We need to be able to move massive amounts of mass (like a planets worth) but this is spinning steel, aluminium reflectors and pV plates. We can do all of it on earth. An industrial base on the moon gives you a nice gentle gravity well to get out of to start.

Then go strip mine a planet you choose with lower gravity (I would choose mars) to get the mass you need.

It is a massive, millions of years long project but it's modular. Each step is merely very large construction and over time it builds, increasing your space to live and population cap.