Backend should support multiple worker processes

Currently, the backend will only work properly when run with a single uvicorn/fastapi worker processes.

It should also support multiple worker processes.

For example the websocket broadcasting mechanism needs to use the redis/valkey.

Start by tracing the backend's websocket broadcasting path and its current uvicorn/FastAPI worker setup. Inspect how Redis/Valkey is used, then verify that multiple worker processes can run correctly and broadcast websocket updates across workers.

Written by the indexing model from the issue text.