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

scripts/gametest/test-game.ts

@@ -0,0 +1,18 @@
+async function main() {
+  const response = await fetch("http://localhost:3000/api/v1/game/start", {
+    method: "POST",
+    headers: { "Content-Type": "application/json" },
+    body: JSON.stringify({
+      source_language: "en",
+      target_language: "it",
+      pos: "noun",
+      difficulty: "easy",
+      rounds: "3",
+    }),
+  });
+
+  const data = await response.json();
+  console.log(data);
+}
+
+main();