Welcome to the forum @steveyeu
Ideally, someone with a Mac who’s done this would help, but the general plan would probably be to have Duplicati run as a privileged user such as root, start as a service at boot time, and be accessible to your entire family. The localhost connection would be available to all, but sharing a Duplicati means they have access to all the family backups, and you’d have to tell other users what limits you want them to respect.
Running as root probably bypasses permissions. If you’re good at groups (UNIX permissions) or access control lists, you could maybe figure out some way that Duplicati could do the job without running as root. There’s nothing too special about it. It’s an application, so it needs to read to backup, and write to restore.
If this all sounds reasonable, then the remaining challenge is the seemingly ill-documented method to get Duplicati running as a service. I’ll point to some past advice while hoping someone who’s done it can help.
MacOS / OSX service installation
Starting Duplicati server-wide (as root) & server-only on the Mac