I don’t think “organic computer” is a good way to think of a brain. The fact that human brains + some scratch paper can implement any Turing-complete model of computation is very interesting. But that’s not true of chimpanzee brains or orca brains or crow brains, all of which belong to intelligent, thinking animals.

Going the other way, it’s not clear that a Turing-complete model of computation can tractably implement (say) crow cognition. Turing machines can solve arbitrary systems of Schrödinger equations, so theoretically we could simulate every atom in a crow’s body and get an AI crow[1]. But that’s obviously intractable for any known physical computer, and would remain intractable even if we moved to proteins rather than atoms. So are there higher-order “primitives” of crow cognition that can be implemented on a Turing machine? Or is the problem akin to integration, where neat “symbolic” solutions are impossible for most brains, and only “numeric” approaches work?

[1] This is also true for humans: even if you take a loopy quantum consciousness approach, AGI is theoretically possible. Sometimes you see people arguing against AGI on the grounds of Gödel-incompleteness, but this is a mystical nonsense understanding of what Gödel actually proved.