Add typecheck

package.json

@@ -13,6 +13,7 @@
     "test": "bun test",
     "lint": "eslint .",
     "lint:fix": "eslint . --fix",
+    "typecheck": "nuxt typecheck",
     "dev:up": "docker-compose -f docker-compose.yml -f docker-compose.dev.yml up -d",
     "dev:down": "docker-compose -f docker-compose.yml -f docker-compose.dev.yml down"
   },
@@ -42,10 +43,11 @@
   },
   "devDependencies": {
     "@nuxt/devtools": "^2.6.2",
+    "@types/bun": "^1.2.20",
     "prettier": "^3.6.2",
     "prettier-plugin-organize-imports": "^4.2.0",
     "prettier-plugin-tailwindcss": "^0.6.14",
     "prisma": "^6.13.0",
-    "vue-tsc": "^3.0.4"
+    "vue-tsc": "^3.0.6"
   }
 }