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.
DietPi-Backup
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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