>>11607585Populations plateau when resources are limited, yes.
At first it would be colonies on the Moon and Mars, then colonies on the gas giant moons, then orbital habitats in the asteroid belt, then orbital habitats being mass produced via strip-mining of planets except maybe Earth, then production of vast numbers of computer satellites like you mentioned.
Each step along the way doesn't get finished before the next step becomes possible to take, someone takes it, and then that group that took the next option zooms ahead in overall capability and power.
Once you can build a rocket on Mars without needing any assistance from Earth, the rest of the solar system is just waiting for you to go take it. Suddenly Earth is not very relevant to most of space colonization.
Once you can build the habitats and vehicles necessary to get out and colonize the moons of the outer solar system, every small object in the solar system becomes 'colonize-able', by acting as feed stock for constructing habitats. The rapidly accelerating production of habitats (directly analogous to bacteria growing on an agar plate) soon overtakes both Earth and the rest of the solar system in terms of human population and overall resources.
In the race to catch up, or merely because they were overwhelmed by millions of orbital habitats in hostile takeovers, more and more of the colonized worlds in the solar system begin to treat their moons and planets like big asteroids, mining up material to launch into orbit to use to build habitats by the millions. Since even a single middle sized moon out-masses the asteroid belt by a significant amount, this group soon becomes the dominant force in the solar system.
At some point while this is happening someone manages to build a computer that can perfectly emulate a human brain. The group that uses this technology to gain low-resource-intensive human brainpower is dominant over any group depending on meat-people, and so soon comes to dominate totally.