How about an actual proning procedure guide?
https://www.moh.gov.sa/Ministry/MediaCenter/Publications/Documents/Prone-position-guidelines.pdf In this it specifically says that the head can be turned left or right. That's what all the google pictures show as well.
As far as surfaces, yes, in a clinical setting of course they're going to use beds and pillows and not put them on the floor. However you've shown me nothing "official" that says that a proning on a hard surface when there's no other alternative would not have any benefits.
Looked all through the guide; missed any mention of kneeling on the back of the patient’s neck or binding their hands behind their back, which puts maximum pressure on their chest cavity. Could you explain to everyone (including the board certified medical doctors) how those contribute to more successful breathing?