I keep seeing those "zero-downtime" tools that really aren't. (This one will wait for app shutdown/startup) They try weird approaches and completely miss that rev-proxies supported this in many ways for ages.

You can live-reload a config, update a link to a Unix socket, update an iptables rule, or do one of many other things that allow you to start the new app version and warm it up before switching new connections to it. Then kill the old one once it's idle. It's safer that way and it stops being a race vs the timeout of new connections.