What you say in confidence stays in confidence.
Your private conversation with the mediator is never shown to your counterpart. This is enforced in the database itself: there is no query a counterpart can run that returns your intake messages or your private assessment.
Only the position summary you explicitly approve crosses to the other side, exactly as you approved it. Until you approve it, nothing crosses at all.
Your reactions to proposals — accepting one, or asking the mediator for changes — stay private. Your counterpart learns you accepted only when they accept the same option, at which point you both see an agreement.
An invite link reveals only the topic of the disagreement. It reveals no position and no conversation.