feat: scaffold quiz API vertical slice

- Add GameRequestSchema and derived types to packages/shared
- Add SupportedLanguageCode, SupportedPos, DifficultyLevel type exports
- Add getGameTerms() model to packages/db with pos/language/difficulty/limit filters
- Add prepareGameQuestions() service skeleton in apps/api
- Add createGame controller with Zod safeParse validation
- Wire POST /api/v1/game/start route
- Add scripts/gametest/test-game.ts for manual end-to-end testing

apps/api/src/app.ts

@@ -4,7 +4,7 @@ import { apiRouter } from "./routes/apiRouter.js";
 
 export function createApp() {
   const app: Express = express();
-
+  app.use(express.json());
   app.use("/api/v1", apiRouter);
 
   return app;