The other commenters have mentioned doing deploys behind a proxy, which is fine, but eventually you're going to have to re-deploy the component that terminates the client connections (i.e. websocket server or SSE, etc).
From the client's perspective, there's not a lot of difference between the server dropping the connection (on redeploy) or the connection being dropped for some other transient reason.
That is to say, with a decent client side handling of connection state you just incrementally rollout your new servers and each server terminates its connections triggering reconnects from the clients.
The hardest part is often maintaining continuity on some stream of events. That is; picking up exactly where you were before the connection dropped. You need some mechanism for the client to report the event it last received, and some way to "rewind" back to that point on the stream.
From the client's perspective, there's not a lot of difference between the server dropping the connection (on redeploy) or the connection being dropped for some other transient reason.
That is to say, with a decent client side handling of connection state you just incrementally rollout your new servers and each server terminates its connections triggering reconnects from the clients.
The hardest part is often maintaining continuity on some stream of events. That is; picking up exactly where you were before the connection dropped. You need some mechanism for the client to report the event it last received, and some way to "rewind" back to that point on the stream.