Claude doesn't even really know about itself: if you ask a question like "can I copy a session to another machine" it will do a web search to read its own documentation then tell you probably not but you can try copying the session files and using a project directory with the same path: might work. I'm not sure I see this as a problem, it's just how things are. I mean humans don't really know what they're thinking either.

How different for ChatGPT - I had some trouble with my harness, and ChatGPT fixed it for me using it's built in skill about ChatGPT's API docs.