feat(api): add auth middleware to protect game endpoints

- Add requireAuth middleware using Better Auth session validation
- Apply to all game routes (start, answer)
- Unauthenticated requests return 401

apps/api/src/routes/gameRouter.ts

@@ -1,8 +1,10 @@
 import express from "express";
 import type { Router } from "express";
 import { createGame, submitAnswer } from "../controllers/gameController.js";
+import { requireAuth } from "../middleware/authMiddleware.js";
 
 export const gameRouter: Router = express.Router();
 
+gameRouter.use(requireAuth);
 gameRouter.post("/start", createGame);
 gameRouter.post("/answer", submitAnswer);