PLEASE NOTE THAT THIS DIFF AND SUBSEQUENT DIFFS IN THIS STACK WILL NOT BE LANDED UNTIL MORE OF THE REDESIGN IS READY SINCE THIS WILL CAUSE REGRESSIONS IN PROD
This diff updates the chat component to use the panel component I introduced earlier. To make things easy to review I only included the changes for the thread list; however, in subsequent diffs I will bring back the message list and house it in this same panel component
Linear task: https://linear.app/comm/issue/ENG-5935/chat-thread-list-ui-redesign
Depends on D10527