To add some background and comments:
From manual section Duplicati.Server.exe
Duplicati needs to store a small database with all settings. Use this option to choose where the settings are stored. This option can also be set with the environment variable
Duplicati.Server.exe is what one typically runs in background. It has no TrayIcon and just a web UI.
The Linux systemd system (administered by systemctl) can run one. It will have trouble doing two.
Run multiple instances of the same systemd unit gives the concept but you might be on your own.
Even more advanced is to see if you can design a start/stop script system to run in your systemd.
Duplicati is designed to somewhat gracefully support start at login for different users on a system,
storing configs in home directories. If started at boot, the usual usage is one shared configuration.
Configuration information is in Duplicati-server.sqlite. Per job databases have randomized names.
Typically for GUI users the DB path is on the Database screen in the
Local database path field.
Exporting a backup job configuration is something you should do anyway, and store that file safely.
The export will be useful if your disk drive is lost, and can also help you set up your moved configs.
I am not set up to test it, but I see an /etc/default/duplicati that looks meant for options via systemd:
# Defaults for duplicati initscript
# sourced by /etc/init.d/duplicati
# installed at /etc/default/duplicati by the maintainer scripts
# This is a POSIX shell fragment
# Additional options that are passed to the Daemon.
You could try putting the --server-datafolder=<path-to-your-chosen-config-folder> there, then restarting.
Duplicati should make a very small Duplicati-server.sqlite there, then you can do the import and Repair.
Though Duplicati-server.sqlite has paths to the per-job databases, the job databases are easily moved.