Push notification_created socket event for instant bell badge updates

Original task: Make the bell badge update instantly when a chat
notification arrives.

Changes:
- artifacts/api-server/src/routes/conversations.ts: After
  createMessageNotifications inserts the rows, emit a
  `notification_created` event to each recipient's `user:{id}` room
  (carrying type/relatedId/relatedType for future routing).
- artifacts/teaboy-os/src/hooks/use-notifications-socket.ts: New hook
  that opens a global socket connection (when the user is logged in)
  and invalidates getListNotificationsQueryKey() and
  getGetHomeStatsQueryKey() whenever `notification_created` fires.
- artifacts/teaboy-os/src/App.tsx: Mounts the hook via a small
  NotificationsSocketBridge component inside AuthProvider so the
  listener is active on every page (home, notifications, services,
  etc.), not just /chat.

Notes:
- Socket join already happens server-side on connect
  (`socket.join('user:{userId}')`), so no API server topology change
  was needed.
- Pre-existing TS errors in api-server and teaboy-os are unrelated to
  this change.

artifacts/api-server/src/routes/conversations.ts

@@ -903,6 +903,15 @@ async function createMessageNotifications(input: {
       relatedType: "conversation",
     })),
   );
+
+  const { io } = await import("../index.js");
+  for (const r of recipients) {
+    io.to(`user:${r.userId}`).emit("notification_created", {
+      type: "chat",
+      relatedId: input.conversationId,
+      relatedType: "conversation",
+    });
+  }
 }
 
 router.post("/conversations/:id/read", requireAuth, async (req, res): Promise<void> => {

artifacts/teaboy-os/src/App.tsx

@@ -3,6 +3,7 @@ import { QueryClient, QueryClientProvider } from "@tanstack/react-query";
 import { Toaster } from "@/components/ui/toaster";
 import { TooltipProvider } from "@/components/ui/tooltip";
 import { AuthProvider } from "@/contexts/AuthContext";
+import { useNotificationsSocket } from "@/hooks/use-notifications-socket";
 import NotFound from "@/pages/not-found";
 import LoginPage from "@/pages/login";
 import RegisterPage from "@/pages/register";
@@ -23,9 +24,15 @@ const queryClient = new QueryClient({
   },
 });
 
+function NotificationsSocketBridge() {
+  useNotificationsSocket();
+  return null;
+}
+
 function Router() {
   return (
     <AuthProvider>
+      <NotificationsSocketBridge />
       <Switch>
         <Route path="/login" component={LoginPage} />
         <Route path="/register" component={RegisterPage} />

artifacts/teaboy-os/src/hooks/use-notifications-socket.ts

@@ -0,0 +1,32 @@
+import { useEffect } from "react";
+import { io } from "socket.io-client";
+import { useQueryClient } from "@tanstack/react-query";
+import {
+  getListNotificationsQueryKey,
+  getGetHomeStatsQueryKey,
+} from "@workspace/api-client-react";
+import { useAuth } from "@/contexts/AuthContext";
+
+const BASE = import.meta.env.BASE_URL.replace(/\/$/, "");
+
+export function useNotificationsSocket() {
+  const { user } = useAuth();
+  const queryClient = useQueryClient();
+
+  useEffect(() => {
+    if (!user) return;
+
+    const socket = io(window.location.origin, {
+      path: `${BASE}/api/socket.io`,
+    });
+
+    socket.on("notification_created", () => {
+      queryClient.invalidateQueries({ queryKey: getListNotificationsQueryKey() });
+      queryClient.invalidateQueries({ queryKey: getGetHomeStatsQueryKey() });
+    });
+
+    return () => {
+      socket.disconnect();
+    };
+  }, [user, queryClient]);
+}