How can we possibly know that the non-connectome details of the brain don't influence computation or conscious experience?
It seems we ignore these only because they don't fit neatly into our piles of linear algebra that we call ANNs.
Sure, to your point, we don't know. But the worm above (nematode) swims and seeks food when dropped into a physics engine.
My main point is that the scale of the human brain is well beyond the capabilities of modern imaging modalities, and it will likely remain so indefinitely. Fascicles we can image, individual axons we cannot. I guess, theoretically, we'll eventually be able to (but it's not relevant to us or any of our remote descendants).
Nematode worms have an oxytocin analogue called nematocin that is known to influence learning and social behaviors like mating. As far as I can find, the project doesn't account for this, or only minimally, but aims to in the future.
It's not surprising that immediate short-term behaviors like movement depend mostly on the faster signaling of the connectome. But since we know of other mechanisms that most definitely influence the connectome's behavior, and we know we don't account for those at the moment, it is not accurate to say that the connectome is "all the information you need".
I agree that mapping the connectome of the human brain is impractical to the point of impossibility. But even if we could, the resulting "circuit diagram" would not capture all the details needed to fully replicate human cognition. Aspects of it, sure. Maybe even enough to make it do useful tasks for EvilCorp LLC while being prodded with virtual sticks and carrots. But it would be incomplete.
There's research on the translation process where cells are basically flash-frozen (to avoid water crystals), then imaged with cryoelectronmicroscopy / AFM etc. where they image the translation process (RNA to protein) in order to get snapshots and get a better understanding of how the folding proceeds and is aided.
If we can image sub-cellular features, what makes you believe we can't trace all the axons, dendrites and the synapses?
It seems more like a question of how to do it cost effectively at scale, not so much a question of "can we or not?".