Another option is to have the client automatically reconnect. That way your backend can just drop the connection when it needs to, and the load balancing infra will make sure the reconnection ends up on a different server.

Of course you do want to make sure the client has exponential backoff and jitter when reconnecting, as to avoid thundering herd problems.

The relevant state will need to be available to all servers as well. Anything that's only known to the original server will be lost as it drops connections. On a modern deployment with a database and probably redis available this isn't too big of an ask.