Disconnect the client if the backend quits

## Development Task

On the serverless tier, when the client is idle for 5 minutes, the backend will quit. But the TiProxy doesn't know the backend quits because it's still reading the client. Then, the serverless tier thinks the connection is still alive and then wakes up a new TiDB instance.

So, TiProxy should always detect the backend and disconnect the client when the backend quits.