So I just updated all server packages (not the minecraft server, rather the operating system etc) and rebooted the server in preparation for the leap-second. There is a certain small chance that a server crashes while the leap second happens. It’s advisable to restart the server manually before that to see if something else would prevent the server from booting up properly. Normally servers like the one we are using is running for months without being rebooted, so it can happen that something sneaks in preventing it from starting properly.
So now that the server seems to be running properly, we can wait for the leap second and hope that everything runs well. There is no risk that something gets damaged, just that the server might freeze and requires a reboot.