There are many ways to do this, but the next up from users is using groups!
For each file or data directory, create a group that owns it. This group should have the service’s user as member. Then create a user for running the backups, and add it to all these groups.
The benefit of this is you don’t have to use root, and you have an association of directory to group that you can always change. You can for example grant a user access to a data directory by just adding it to its group.