> But how are animals with nerve-centres or brains different?

In current LLM neural networks, the signal proceeds in one direction, from input, through the layers, to output. To the extend that LLM's have memory and feedback loops, it's that they write the output of the process to text, and then read that text and process it again though their unidirectional calculations.

Animal brains have circular signals and feedback loops.

There are Recurrent Neural Network (RNN) architectures, but current LLM's are not these.