In principle one could imagine a processor design that works on these intermediate states that somehow vastly exceeds the computational power of a modern system despite using the same base transistors; in practice we have no idea how to build such a thing, and if we did, we wouldn't know how to build a second one of the same thing reliably either.
Biology lacks this restriction. That doesn't mean it's pure and utter chaos, either, there's bounds on that because it still needs systems to at least be metastable. But where humans engineer almost exclusively with stable systems, biology freely uses metastable systems all over the place. And then, even more remarkably, it deals with the question of how to replicate such a strange system in a way that no modern human engineer ever would by making every instance unique, and still somehow functional.
It's a tough act to follow.
Often the most efficient solution to a problem ends up being a simple one. It would be very surprising if the human brain's Rube Goldberg machine was anywhere near close to a mathematically optimal implementation of intelligence.
It's possible that much of the complexity in a biological neuron is simply working around other complexity introduced by biology, solving problems that we programmers do not even have to think about because we can simply directly use matrix multiplication.
Humans can attempt to multiply numbers and frequently get the wrong result. That doesn't scream "pushing the limits of intelligence".
So I tend to err on the side of biology being more complex than not.
But it's absolutely possible that the high-level behaviour is simple while the underlying implementation is complex and chaotic, as in the gas laws.