Assuming the traditional stateless routing of requests, say round robin from load balancers; how do you make sure the returning UI client ends up on the same backend server replica that's hosting the conversation?

Or is it that all your tokens go through a DB anyway?

It's fairly easy to keep an agent alive when a client goes away. It's a lot harder to attach the client back to that agents output when the client returns, without stuffing every token though the database.