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).