This is not the case.

I use OpenAI a lot on the paid plan via the UI. It now knows absolutely loads about me and seems to have a massive amount of cross conversational memory. It's really getting very close to what you'd expect from a human conversation in this regard.

Sure the model itself is still stateless, and if you use the API then what you say is true.

But they are doing so much unseen summarisation and longer context building behind the scenes in the webapp, what you see in the current conversation history is just a fraction of what is getting sent to the model.