My wife and I have noticed that our old 2017 Macbook Air behaves differently depending on who’s logged in. That’s running Monterey, so it has nothing to do with Apple Intelligence, but I wouldn’t be surprised if apps like Firefox (the browser we use) and Google would keep track of personal choices so it behaves differently for the two of us.
Yes, there’s a lot of information that’s stored on a per-account basis, but I can’t figure out what that would be for Apple Intelligence since something like summarization is system-wide.