Backup and Restore to network?

yes indeed the backup location needs to be capable allow Linux permissions. You could using NFS on your Synology. On my test it was working well.

https://www.synology.com/en-global/knowledgebase/DSM/tutorial/File_Sharing/How_to_access_files_on_Synology_NAS_within_the_local_network_NFS

 DietPi-Backup
─────────────────────────────────────────────────────
 Mode: Backup

[  OK  ] DietPi-Backup | DietPi-Userdata validation: /mnt/dietpi_userdata
[ SUB1 ] DietPi-Services > stop
[  OK  ] DietPi-Services | stop : cron
[  OK  ] DietPi-Backup | Free space check: path=/mnt/nfs_client/data | available=2145406 MiB | required=3208 MiB
[ INFO ] DietPi-Backup | Backup to /mnt/nfs_client in progress, please wait...
sending incremental file list
    631,840,097  98%    1.36MB/s    0:07:23 (xfr#17866, to-chk=0/23106)

sent 633,288,016 bytes  received 371,441 bytes  1,412,841.60 bytes/sec
total size is 643,018,702  speedup is 1.01
[  OK  ] DietPi-Backup: Backup | Completed