feat: add real-time notification system and fix admin login bug

- Fix login: role field was missing from session (admin page inaccessible)
- Add onlineUsers map in socket/state.ts to track connected users
- Join personal user:${id} socket room on connect for targeted notifications
- Emit friendRequestReceived/friendRequestAccepted socket events from friends controller
- Add sendGameInvite socket event handler on server
- New NotificationContext: global socket provider for registered users
- New NotificationPanel: bell icon with unread badge and dropdown in header
- Friends page: inline game invite input per friend with sendGameInvite

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

server/src/socket/index.ts

@@ -11,6 +11,7 @@ import {
     leaveLobby,
     sendMove
 } from "./game.socket.js";
+import { onlineUsers } from "./state.js";
 
 const socketConnect = (socket: Socket) => {
     const req = socket.request;
@@ -25,7 +26,28 @@ const socketConnect = (socket: Socket) => {
         });
     });
 
-    socket.on("disconnect", leaveLobby);
+    // Track online users and join personal notification room
+    const userId = req.session.user?.id;
+    if (userId && typeof userId === "number") {
+        onlineUsers.set(userId, socket.id);
+        socket.join(`user:${userId}`);
+    }
+
+    socket.on("disconnect", () => {
+        if (userId && typeof userId === "number") onlineUsers.delete(userId);
+        leaveLobby.call(socket);
+    });
+
+    // Forward game invites to target user's personal room
+    socket.on("sendGameInvite", ({ toId, gameCode }: { toId: number; gameCode: string }) => {
+        const fromUser = req.session.user;
+        if (!fromUser?.id || typeof fromUser.id === "string") return;
+        io.to(`user:${toId}`).emit("gameInviteReceived", {
+            fromId: fromUser.id,
+            fromName: fromUser.name,
+            gameCode
+        });
+    });
 
     socket.on("joinLobby", joinLobby);
     socket.on("leaveLobby", leaveLobby);