Desktop-only tab bar above the chat screen, one tab per open
conversation or new-chat tab. The active tab follows the route id;
clicking navigates, middle-click or the close button closes (switching
to the left neighbor), and a trailing + starts a new chat. Tabs appear
only on chat-id routes; the bare #/ new-chat view has none. The bare
route stays put unless a prompt/model deep-link routes it to a new-chat
tab.