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/controllers/gameController.ts

@@ -1,8 +1,17 @@
 import type { Request, Response } from "express";
-import { prepareQuestions } from "../services/gameService.js";
+import { GameRequestSchema } from "@glossa/shared";
+import { prepareGameQuestions } from "../services/gameService.js";
 
-export const getGame = async (req: Request, res: Response) => {
-  const query = gameRequestSchema.parse(req.query);
-  const questions = await prepareQuestions(query);
-  res.json({ success: true, data: questions });
+export const createGame = async (req: Request, res: Response) => {
+  const gameSettings = GameRequestSchema.safeParse(req.body);
+
+  // TODO: remove when global error handler is implemented
+  if (!gameSettings.success) {
+    res.status(400).json({ success: false });
+    return;
+  }
+
+  const gameQuestions = await prepareGameQuestions(gameSettings.data);
+
+  res.json({ success: true, data: gameQuestions });
 };