feat: add orchestrator admin action interval and integrate game engine dependency

app/gateway-api/package.json

@@ -20,6 +20,7 @@
         "@fastify/cors": "^11.2.0",
         "@prisma/client": "^7.2.0",
         "@sammo-ts/common": "workspace:*",
+        "@sammo-ts/game-engine": "workspace:*",
         "@sammo-ts/infra": "workspace:*",
         "@trpc/server": "^11.4.4",
         "date-fns": "^4.1.0",