In might be computable in principle but not in practice for a long time, similar to how it is possible to simulate all molecules of air in one cubic meter (neglecting quantum effects), but not actually feasible in practice. Any argument for computability all needs an argument why a "coarse graining" or "effective model" of the underlying physical system exists.
In the case of transistors that is because all that matters are binary stable states, which reliably abstract over the complicated device physics. In the case of biological cells and neurons in the brain it is much less obvious what the reliable abstraction is. Right now a lot points towards "it is just a bunch of linear algebra and lots of data", but especially when we come to things like memory, online and few shot learning, the answer becomes far less obvious.
In the case of transistors that is because all that matters are binary stable states, which reliably abstract over the complicated device physics. In the case of biological cells and neurons in the brain it is much less obvious what the reliable abstraction is. Right now a lot points towards "it is just a bunch of linear algebra and lots of data", but especially when we come to things like memory, online and few shot learning, the answer becomes far less obvious.