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/tsconfig.json

@@ -2,7 +2,7 @@
   "extends": "../../tsconfig.base.json",
   "references": [
     { "path": "../../packages/shared" },
-    { "path": "../../packages/db" }
+    { "path": "../../packages/db" },
   ],
   "compilerOptions": {
     "module": "NodeNext",
@@ -10,7 +10,7 @@
     "outDir": "./dist",
     "resolveJsonModule": true,
     "rootDir": ".",
-    "types": ["vitest/globals"]
+    "types": ["vitest/globals"],
   },
-  "include": ["src", "vitest.config.ts"]
+  "include": ["src", "vitest.config.ts", "../../packages/db/src/models"],
 }