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>

types/index.d.ts

@@ -93,6 +93,18 @@ export interface TournamentPlayer {
     gamesPlayed?: number;
 }
 
+export type NotificationType = "friendRequest" | "friendAccepted" | "gameInvite";
+
+export interface AppNotification {
+    id: string;
+    type: NotificationType;
+    fromId: number;
+    fromName: string;
+    gameCode?: string;
+    createdAt: number;
+    read: boolean;
+}
+
 export interface TournamentRound {
     id?: number;
     tournamentId?: number;