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/routes/gameRouter.ts

@@ -4,4 +4,4 @@ import { createGame } from "../controllers/gameController.js";
 
 export const gameRouter: Router = express.Router();
 
-gameRouter.get("/", createGame);
+gameRouter.post("/start", createGame);