Prone position is recommended because the breathing action is mainly through the back, not the front, so lying on one's stomach, even for mild forms of CV, is a more effective way of taking in O2. It frees up the rib cage and increases the capability of the muscles around the ribs, as the virus compromises muscle movement (because everything aches).
They recommend deep breathing through the back, including if you are at home and trying to manage your symptoms within the first 7days.
Definitely don't spend long periods lying in your back is the advice I've heard.