Does sentience need memory? I would say it's orthogonal. There are examples of people in the real world who only remember things for about 3 minutes before they lose it. They can't form any real memories. These people are still sentient despite lack of memory. See: https://www.damninteresting.com/living-in-the-moment/
If chatGPT was sentient, I would say it has nothing to do with the 4000 character limit. The 4000 character limit has more to do with it's ability to display evidence of "sentience".
It also functions as memory in practice, though. With some complex tasks that can be broken down into steps, it often makes a big difference if you tell GPT to summarize its "understanding" of the current state as it goes through those steps - by repeating a phrase, keeping it within the token window, it effectively "remembers" something.
If chatGPT was sentient, I would say it has nothing to do with the 4000 character limit. The 4000 character limit has more to do with it's ability to display evidence of "sentience".