But for biological neurons to do something that can't be efficiently approximated on a digital computer (but conductive to useful information processing) they need to have unknown unknowns (well, partial unknowns like an unknown quantum algorithm will do too).

We don't know the violations of the physical Church-Turing thesis that are conductive for machine learning. We don't have evidence for their existence in the brain (although, the brain would be the prime candidate for finding them as evolution works directly with the true physical laws).

BTW, large ANNs don't try to model how the brain does things. They are trying to mimic what the brain does. So, using "how many transistors/artificial neurons it takes to model a biological neuron" is not a good approach.

We have no evidence. We even have no solid theories how this can work (Penrose's OrchOR is "OrchOR somehow taps into mathematical knowledge somehow encoded into the structure of spacetime"). But people, for some reason, insist that there should be something there. I can't attribute it to anything else but to deeply entrenched feeling of human exceptionalism.

You're talking about a philosophical debate whether the brain is computable, the other commenters are pointing out that even conservative estimates point to a brain-like NN requiring over a quadrillion parameters.