As I've already read on the sub the Android interface is 1080p but Prime Video won't give me any option to watch shows in 4K. On the other hand youtube gives me the chance to switch to 4K although I'm not sure that's the real resolution output. Is there any possibility 4K is only available through HDMI? Am I missing something?
Prime offers separate versions of the same content in different resolutions. Use the applications search function and type in "uhd". That should give you results with content that is available in 4K.