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/lib/auth.ts

@@ -1,9 +1,11 @@
 import { betterAuth } from "better-auth";
 import { drizzleAdapter } from "better-auth/adapters/drizzle";
 import { db } from "@glossa/db";
+import * as schema from "@glossa/db/schema";
 
 export const auth = betterAuth({
-  database: drizzleAdapter(db, { provider: "pg" }),
+  database: drizzleAdapter(db, { provider: "pg", schema }),
+  trustedOrigins: ["http://localhost:5173"],
   socialProviders: {
     google: {
       clientId: process.env["GOOGLE_CLIENT_ID"] as string,