Duplicati.Library.AutoUpdater.exe sounds like it does what you want, though I haven’t tested it for your use. The GUI autoupdater has a bug where a Windows service install needs a service restart. Other situations appear to be handled better by the GUI autoupdater, so perhaps the command line one will also work well.
If you prefer doing things remotely (just not using the web interface), there’s a third-party Duplicati client to access the internal web interface, while providing a command line interface for your scripting or whatever.