I think Synology works very well as a Time Machine solution. It works as any other, and the Mac doesn't really know that its a Synology. You simply enable the Time Machine function of Synology, set up a Time Machine Folder, and then connect Time Machine on your Mac to that folder.
I have had issues with my Mac losing connection to the Synology from time to time, and there seems to be no particular reason for this, but disabling the power saving features on the Synology seemed to help. (keep it from sleeping)
You can migrate your data: https://support.apple.com/en-us/HT202380
Set up Synology: https://www.synology.com/en-global/knowledgebase/DSM/tutorial/Backup/How_to_back_up_files_from_Mac_to_Synology_NAS_with_Time_Machine
While the Synology is good, I found, it, just like nearly all such solutions seem to eventually get lost, especially with wifi-based backups. This often corrupts the backup. For systems that are always on and connected via ethernet, I have never had any issues with any device, but laptops, which get abruptly disconnected, seem to cause Time Machine issues over time.
Opinion: Cloud-based backups seem to handle these interruptions in stride and therefore I have migrated fully to a cloud solution. More expensive? yes, in the long run, but stable and dependable. Never a corruption in now 3 years of cloud backups.