Stream processing is becoming increasingly essential for extracting business value from data in real-time. To achieve strict user-defined SLAs under constantly changing workloads, modern streaming systems have started taking advantage of the cloud for scalable and resilient resources. New demand opens new opportunities and challenges for state management, which is at the core of streaming systems. Existing approaches typically use embedded key-value storage so that each worker can access it locally to achieve high performance. However, it requires an external durable file system for checkpointing, is complicated and time-consuming to redistribute state during scaling and migration, and is prone to performance throttling. Therefore, we propose shared storage based on LSM-tree. State gets stored at cloud object storage and seamlessly makes itself durable, and the high bandwidth of cloud storage enables fast recovery. The location of a partition of the state decouples with compute nodes thus making scaling straightforward and more efficient. Compaction in this shared LSM-tree is now globally coordinated with opportunistic serverless boosting instead of relying on individual compute nodes. We design a streaming-aware compaction and caching strategy to achieve smoother and better end-to-end performance.