New install cannot find existing backup

According to man systemd.unit (linked above or available using man command), .wants has symlinks.
Possibly you were running /lib/systemd/system/duplicati.service, and had edited it. You can look at file.

I think the problem with editing Duplicati-installed files directly is that the next install will overwrite yours.

How can I make a modification to a .service and keep it persistent? [duplicate]
Where to place user created systemd unit files [duplicate]

Running Google search for systemd "different user" led me to some top hits matching my advice:

How do I create a service on CentOS running as a different user than root? is basicaly the same recipe.
How to change service user in CentOS 7? suggests systemctl daemon-reload also. Sounds proper.

man systemctl talks about what that does, and finding it also led me to systemctl edit which does it automatically after you edit the configuration. You could maybe systemctl edit --full duplicati, pulling up the old file and letting you add the User= and Group= lines that give your own user and group.

There seems to be a fancier way to override settings, if you omit --full. It looks like you still need section.
Or at least the forum post here explicitly gave it. You could test omitting that, but probably safer to give it.

Editing a Unit File
How To Use Systemctl to Manage Systemd Services and Units Especially look at Editing Unit Files

If you look at your duplicati.service files, you’ll probably see some lines looking like below:

[Service]
Nice=19
IOSchedulingClass=idle
EnvironmentFile=-/etc/default/duplicati
ExecStart=/usr/bin/duplicati-server $DAEMON_OPTS
Restart=always

That’s your Service section. You want to add lines like below:

User=<your user>
Group=<your group>

but I have no idea if that’s what your 18.04 does. You can look. There are other ways to get what you got.
The lack of comment on manual start implies start at boot, but systemctl status duplicati willl say.
You can also use ps to see what user it is. If it’s root, you might have used –server-datafolder to set that durectory to your home directory, then accessed it as root (and put up with lower security to run as root).