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

packages/db/src/index.ts

@@ -9,3 +9,5 @@ config({
 });
 
 export const db = drizzle(process.env["DATABASE_URL"]!);
+
+export { getGameTerms } from "./models/termModel.js";