If backup history (older archives) of the apps / system are not required:
Backup of borg_server app on old and restore on new server (without migration of the archives) is easier than migrating the archives manually.
If the ssh config is correctly adapted on the server to be backup, the borg_ynh will create a new backup on the new server. Which probably takes as much time as migrating the last archive from the old to the new server.
Except maybe if you can transfer from old to new backup server over the local network (which is my case but I have a good enough internet connection).