Isn't there a way to react to a silent push notification when a Mac app isn't running?

It's documented that application(_:didReceiveRemoteNotification:) is only called when the app is running in AppKit.

https://developer.apple.com/documentation/appkit/nsapplicationdelegate/application(_:didreceiveremotenotification:)

application(_:didReceiveRemoteNotification:) | Apple Developer Documentation

Tells the delegate when the app receives a remote notification.

Apple Developer Documentation
@simonbs I don’t think so. There’s no background state for Mac apps. If your app isn’t running the system will not start it to handle a notification.