The context is state. This is especially noticable for thinking models, which can emit tens of thousands of CoT tokens solving a problem. I'm guessing you're arguing that since LLMs "experience time discretely" (from every pass exactly one token is sampled, which gets appended to the current context), they can't have experiences. I don't think this argument holds - for example, it would mean a simulated human brain may or may not have experiences depending on technical details of how you simulate them, even though those ways produce exactly the same simulation.
The context is the simulated world, not the internal state. It can be freely edited without the LLM experiencing anything. The LLM itself never changes except during training (where I concede it could possibly be conscious, although I personally think that's unlikely).