feat: implement competitive clicker MVP with Colyseus.js

- Add real-time multiplayer game server with Colyseus
- Implement unique player naming system with auto-increment
- Create lobby system with automatic matchmaking
- Build 10-minute competitive clicking game rooms (max 2 players)
- Add admin dashboard for game management (pause/resume/restart/kick)
- Implement Vue 3 client with professional UI
- Add WebSocket communication with state synchronization
- Include TypeScript throughout with proper typing
- Create REST API for admin operations
- Add reconnection support and error handling

shared/types.ts

@@ -0,0 +1,27 @@
+export interface PlayerInfo {
+  sessionId: string;
+  name: string;
+  clicks: number;
+}
+
+export interface RoomStats {
+  roomId: string;
+  players: PlayerInfo[];
+  gameStatus: GameStatus;
+  timeRemaining: number;
+  winner?: string;
+  createdAt: number;
+}
+
+export enum GameStatus {
+  WAITING = 'waiting',
+  PLAYING = 'playing',
+  PAUSED = 'paused',
+  FINISHED = 'finished'
+}
+
+export interface AdminAction {
+  action: 'pause' | 'restart' | 'kick';
+  roomId: string;
+  playerId?: string;
+}