RisingWave Community - Does RisingWave support maintaining persistent websocket connection, data processing, and data storage?

RisingWave can maintain persistent connection with reconnect logic for supported sources. For more details, check https://docs.risingwave.com/docs/current/data-ingestion/ for all supported sources.
RisingWave is responsible for data processing.
RisingWave can maintain storage for both your target data and internal states with Materialized View. Check https://docs.risingwave.com/docs/current/sql-create-mv/ for more details.