First of all, there needs to be a much easier way to provide feedback and suggestions. I put UI experience first.
My suggestion: The left sidebar should optionally group chats by Project, with collapsible sections. Right now, all chats appear in one list, making it difficult to know which project a chat belongs to. I often have to click back to Projects just to make sure I’m entering the correct one. Grouping chats by project would reduce clicks and cognitive load.