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Humanity taken as a whole doesn't participate in trade with any other entities. A smart AI might be able to reproduce and produce legs and arms comparable to that of humanity as a whole not just compared to single individual humans.

Humanity doesn't need to be given space ship blueprints from outside. But maybe the AI also is able to do research. You can also think that the Ai might at some point make humanoid robots with 2 robots per 1 person alive. Does it at that point matter if humanity doesn't cooperate? Well before it has 2 robots per 1 person it probably has 1 robot per 1 person. Can it go to 2 robots per person without the help of humanity? Quite possibly. If it manages to do the first robot can't it just iterate that to get to the 6 miljard robots? It needs a lot of materials for that and all mines are human controlled. But what prevents it from building its own mines?

Humans might be dependant on the market of human civilization but an autonomous robot can start a separate market on its own. And that market can possibly grow larger than the human market at some point for it has different properties than the human market.