Restarts without downtime are technically possible, using both canary deployments and persistent state.

However, the state doesn't need to be persistent. We can actually offload this to the clients.
Upon shutting down, the clients receive a signed payload with the gamestate, that is only valid for a short timeframe.

Upon re-establishing the connection, the client sends this payload, which the server uses to reconstruct the lobby state.

This way, we can prevent abuse, won't need persistent storage and can still survive a restart.