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I do not believe there is a way to disable the changing of the notification icon, but you could potentially run Duplicati without the tray icon entirely. Instead of running Duplicati.GUI.TrayIcon.exe at startup, run Duplicati.Server.exe instead.
Alternatively you could get VSS working properly. Even though you have snapshot-policy set to Auto, it may not be using VSS. The Duplicati process has to run with elevated administrative rights in order to use the snapshot feature.