Well, the OP already has a NAS. So the point is how to use it. Sure, if you don’t, that’s a waste of money just for a backup.
As I thought about this, backing up music from the NUC to the Synology may be a moot point. I do this with ActiveBackup. But I understand some older or under-powered Synology machines don’t support ActiveBackup.
One may be able to do that with rsync, but that’s beyond my skill level.