Is it too anthropomorphic to say that this is a lie? To say that the hidden state and its long term predictions amount to a kind of goal? Maybe it is. But we then need a bunch of new words which have almost 1:1 correspondence to concepts from human agency and behavior to describe the processes that LLMs simulate to minimize prediction loss.
Reasoning by analogy is always shaky. It probably wouldn't be so bad to do so. But it would also amount to impenetrable jargon. It would be an uphill struggle to promulgate.
Instead, we use the anthropomorphic terminology, and then find ways to classify LLM behavior in human concept space. They are very defective humans, so it's still a bit misleading, but at least jargon is reduced.
These LLMs are almost always, to my knowledge, autoregressive models, not recurrent models (Mamba is a notable exception).
Intermediate activations isn't "state". The tokens that have already been generated, along with the fixed weights, is the only data that affects the next tokens.
The 'hidden state' being referred to here is essentially the "what might have been" had the dice rolls gone differently (eg, been seeded differently).
Processing tokens is a bit like ticks in a CPU, where the model weights are the program code, and tokens are both input and output. The computation that occurs logically retains concepts and plans over multiple token generation steps.
That it is fully deterministic is no more interesting than saying a variable in a single threaded program is not state because you can recompute its value by replaying the program with the same inputs. It seems to me that this uninteresting distinction is the GP's issue.