feat(FN-1957): add inbox/outbox sub-tabs to agent mailbox views

- Split agent mailbox responses into inbox and outbox arrays while keeping messages as an inbox alias
- Add Inbox/Outbox sub-tabs in MailboxView and MailboxModal with unread badge and agent-switch reset behavior
- Render tab-specific empty states and sent-message metadata in the outbox list
- Add dashboard styles and mobile overrides for agent mailbox sub-tabs
- Expand MailboxModal and MailboxView tests to cover sub-tab visibility, switching, reset, and unread badge behavior

packages/dashboard/src/routes.ts

@@ -17272,7 +17272,8 @@ export function createApiRoutes(store: TaskStore, options?: ServerOptions): Rout
       const agentId = req.params.id;
       const mailbox = await msgStore.getMailbox(agentId, "agent");
       const inbox = await msgStore.getInbox(agentId, "agent");
-      res.json({ ...mailbox, messages: inbox });
+      const outbox = await msgStore.getOutbox(agentId, "agent");
+      res.json({ ...mailbox, messages: inbox, inbox, outbox });
     } catch (err: unknown) {
       if (err instanceof ApiError) {
         throw err;