If you are at that scale then surely you put up some load balancers which can look at the client request (eg a request header `Accept-Version: abc123` or whatev

If you are at that scale then surely you put up some load balancers which can look at the client request (eg a request header `Accept-Version: abc123` or whatever) and route it to the correct backend server that can handle the request. If you're not at that scale ie if your app deploys in a few seconds then just forcing a reload seems like a perfectly feasible strategy.