There is no "thousand colonies". There
might be
one colony, and that might not ever be self sufficient.
Interstellar travel is a physics problem, not an engineering one. Even make believe nuclear propulsion is still aggressively limited by the rocket equation and still wont get you anywhere in a meaningful time frame.
There will never be an interstellar empire. It will never make sense to do trade between two planets that are otherwise capable of producing things, because the energy cost of doing anything in space absolutely dwarfs any possible industrial process. It doesn't matter how low quality your local iron ore is, importing ore from a different planet will never be a better option because transportation costs are effectively infinite.
Human trade is almost entirely based on the fun quirk that sea based transportation is ludicrously efficient, such that you can ship a single pound of product all over the globe and it can still be cheap. The physics of space are essentially the opposite of the physics of sea travel, in that it is dramatically harder and more energetically expensive than almost anything else you can do, and the energy regime it operates in will dwarf any other consideration.
If there was a magical way to turn joules directly into a change in kinetic energy, as in a machine that could magically extract every joule of "energy" from matter in an E=mc^2 way and directly reduce an object's kinetic energy by that much, taking a 100 kilogram human up to half the speed of light and eventually slowing them down again would take 31 kilograms of matter to "burn", and you have to accelerate all that matter too. That matter would require another like 10kg of matter to "burn" and then you have to accelerate that matter too and so on and so on.
And we do not come even remotely close to any mechanism, real or theoretical, that could convert mass to a change in kinetic energy. Even if you had like a magic antimatter machine that could come very close to turning a gram of matter into it's entire "energy" content, ways of turning thermal or electrical energy into thrust have their own inefficiencies, difficulties, and do not even come close to mapping to "Each joule of energy equals a joule of kinetic energy change".
And even with our magic spacecraft machine that cheats physics, that's still an 8 year round trip to Alpha Centauri and back, with something like a 50%-65% payload fraction.
The scale of things in space combined with the nature of that space makes interstellar anything nonsensical. Even interstellar travel of just information is fairly mediocre. SciFi will never exist in our world, and at this point should probably just be called "Fantasy with more plastic"