There are lot of software and hardware that use biomimicry.

Schmitt trigger, one of the fundamental components in electronics is based on nature (and its creator is called as the father of biomimicry/ biomimetics https://ehistory.osu.edu/exhibitions/biomimicry-a-history).

Swarm optimization algorithms (genetic algorithms, particle swarm optimization, Ant Colony optimization etc) are more openly based on nature.

Neural networks in their current implementation don't even come close to the complexity and computational power of a single real neuron. While that is the case, on an extremely basic level they are designed after concepts learned about real neuronal networks

I do mean extremely basic I can't emphasize this enough, so much so that I normally say its not even close