There are no features in Duplicati that will “wake” the computer if it is in standby mode.
If you have a single-user machine, you can use the Duplicati server with something like:
> sudo systemctl enable duplicati
> sudo systemctl restart duplicati
This will cause Duplicati to run in the background as a service.
You can then connect to it from the tray-icon with:
> duplicati --no-hosted-server --hosturl=http://localhost:8200
If you don’t like the tray-icon, you can just add a bookmark in your browser.
That said, if you have configured a backup at night, the backup should run when you start Duplicati (on login). There is a 5min delay (can be configured from settings) that is inserted to make sure networks etc. are up before running the backups.