No they don’t have memories. With an harness you just send historic data into the prompt.
Why, exactly, is this distinction relevant? The brain must store episodic memory somewhere too. From a cursory read, it seems to me that our experiences are processed through the hippocampus and amygdala into a high-level annotated encoding of historical data, stored somewhere else (unclear), fetched based on various triggers, replayed and reinterpreted by the neocortex, and, I assume, sent back through the hippocampus once more for updating. Sure, it's all in the brain, but I don't think physically separating the storage makes it fundamentally different.
I mean, I've replayed old memories in my head before. Sound, image and all. That's kind of like sending historic data into a prompt, isn't it? Of course it's not exactly the same thing, but the difference isn't exactly load-bearing, if you'll excuse the claudism. I feel like we're grasping at straws.
Memory is definitionally the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. There's no special carve out for 'except when it's an LLM.'
There's no inherent, technological reason to feed the historic data into the prompt, though. You could train a network with a second input for model-states, and during inference, feed into that input historic model-states that occured for the same LLM when consuming input that is somehow associatively related to whatever input is currently being consumed. Can you definitely show that this would be meaningfully different from how humans "experience" memories?