Let's say that the upgrade proces is more or less independent from the move from one server to another. You can do the upgrade before moving the bareos installation or after - it's your call.
Unfortunately, due to many possible variants of configuration (dir, sd, fd on the same machine or maybe sd on another one? single sd, multiple sd's? client-initiated connections? moving to another ip/hostname or scrapping old machine and reusing its network parameters? do you encrypt backups?), it's not easy to give a simple step by step scenario.
The easiest situation would of course be if you wanted to do a switch "in-place" - then you'd probably mostly copy the bareos daemons' configuration, spool files, device files (if you're using file-based storage), database configuration and data and you'd be pretty much set.