Answering my own question here just in case someone reads this with the same problem.
In my case the problem was, that I was not aware, that a collegue of mine not only converted from AppDelegate to SceneDelegate, but also converted the app to a SwiftUI app. DUH!
In case of a SwiftUI App the deeplink will be sent to the swiftUI view in the WindowGroup, inside the body of the SwiftUI.App!
So just adding an onOpenURL() modifier is enough to receive the deeplink event, when the app is running in the background.
Case closed. :-)
sfalex
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