I realize that teams are the target audience that "keeps the lights on", but would it be possible to hide the team permission when a user isn't part of any team? I'm now seeing "🔒 Private" on all of my notebooks (followed by "🔗 Link shared" or "🌐 Published" for shared notebooks).

Yes, we hear the feedback and are looking into how to make this more clear.

We are not showing the 'Private' anymore on personal notebooks.