I see. So basically you have to keep the service running across the upgrade and then wait for it to shut down due to inactivity, then be restarted by systemd to make the update apply. Or alternatively you could make the app detect that it's been updated, stop accepting new connections, finish servicing the old connections, and then shut itself down once all existing connections are finished. On restart it'd then be using the new code, re-accept the socket from systemd and start accepting again.
I guess this can work for quiet services that are safe to change on disk because they open everything at startup and never close or re-open the fds, or if there's a snapshotting layer on top.
