this is a hack I have used and am proud of:

if you use Caddy as your reverse proxy (instead of nginx for example which does not do this), when requests come in and your service is missing because it's being deployed, Caddy waits for a timeout before giving up. this means that visitors during the brief deploy period don't see errors - they just get a slightly longer wait, which often is not obvious depending on how long your service takes to boot.