Maybe with their state being fixed in time; LLMs do not change

Not with agents and chain of thought. Agents can run for hours continuously. So sure, an AI agent is not the same as a sentient human on the time scale of a year, but on the time scale of a few hours, perhaps the AI is "sentient".

The first paper you linked is focused on the mechanism and not the output. It creates a definition of "thought" and then talks about how the AI doesn't "think in the feature space". It only addresses chain of thought at the end, and says that the issue is that it constrains AI to think in natural language only (instead of, say, pictures).

But again, why would thinking in pictures define sentience? The paper gives a rock-paper-scissors example and says that the AI thinks about it in a different way than a human. So what? If a human plays rock paper scissors against the AI and the AI's output is indistinguishable from a human's, 99.9% of the time, why is that not sentient?

This is like saying python programmers are not real programmers. If a python programmer can implement the same program in python, who cares what language they use.

I'd love for a better definition of sentience than "it works differently than humans".