I believe that the only FS that absolutely need to be on the root partition are /etc and /var. The rest can be anywhere else with various degrees of tinkering. For /home to be moved, you should just need to edit your fstab (or your systemd mounts, depending on your distro).
I’d not recommend Synology anymore, as they’re starting to implement vendor lock on their drives and NAS boxes. As in, you’ll have to use their drives for the Nas to work.