I attempted to screenshot the whole phone screen using taifun's extension, but it doesn't work as I need. Is there another extension, or way to use this one to screenshot the whole phone - even when you have the app running in the background - even if you are running another app?
you can't take a screenshot of other apps like this
this requires a service running in the background, see also https://stackoverflow.com/a/47097901/1545993
you could write your own extension and create the functionality yourself...
more information about how to create an extension see the App Inventor Extensions document
however that will be more advanced and will require some Java skills...