Indeed the issue only exists on my emulator in Android Studio.

On real devices the network operations in the background work flawlessly, too. The WorkManager work even "works" when the app is completely closed.

So the reason for this issue seems to be that emulators might handle network access differently than real devices when apps are in the background.

This is weird and not officially documented as far as I know.

So, when in doubt, test your app on a real device to check whether the problem also exists in the field and not just in the emulated development environment.