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Depends how technological evolution is capped.
1) Putting every single independent mind in a simulation, with robots programmed to maintain, expand, and fuel the physical hardware for trillions of years. No way to cause problems if things with free will only exist in a simulation.
If the purpose of the simulation is to provide a happy and fulfilling life to beings with a human mindset and human values, that's easy: Just invent a world where people believe it's the real world, and have it be utopian as the default state but cleverly nudge things around to create countless simultaneous story arcs that appear to have actual stakes, but end with everyone safe and happy. Basically it's putting the entire population into a children's cartoon.
2) What I like to call the Planescape approach, since it's very similar to the D&D setting of the same name. Magic replaces and prevents advanced technology, and magic is subtle manipulations of a field managed by AIs that have been allowed to self-develop to the point of maximum technological advancement. Making sure the AI filling this role is safe should be easy, they're only dangerous when people can create them carelessly or malevolently.
If everyone can use magic, this puts everyone on very equal footing.
It should be fairly easy to make this play out like option 1, although since actual matter and energy is being used the scenario can't last as long (unless the big rip happens) and a lot less can be done.
3) Simply having the same AIs as in option 2, but they just interfere occasionally to prevent humans from inventing anything too dangerous.
Humans build spaceships and expand freely across the cosmos in this case, and are able to wield very advanced technology with certain limits.
This is the shittiest option, because humans are shitty and this gives humans the most control.
Personally I think option 1 is best, but option 2 is a good substitute if humans aren't cool with being trapped in a simulation.
