I tried building something similar a few months ago. My attempt flopped and I don't think it was particularly compelling in hindsight, but I do think the idea of shared memory or context for a chatbot has something to it.

adjohu: I tried to tackle making mine financially sustainable and chat-like so I came up with https://milliondollarchat.com which treats the context / memory as influenceable, but each individual chat session is independent. Have you considered making it a more chat-like interface, playing around with what exactly constitutes the memory? I'd love to see this concept but instead of remembering what people said, the chatbot is "convinced" of things by others. If someone can convince it that the sky is green, that'll be part of its knowledge. Each chat session would be sort of... pvp chat, the text version of r/place.