Recovery Position
Standard first aid for an unconscious person (after checking their ABC - Airway, Breathing, Circulation), is to lie them on their side.
The choking danger is worse when lying on the back.
For someone in a spacesuit, with backpack, sideways on a stretcher would probably be best, but you'd need to tie them in place to stop them rolling off.
Alternatively, put a couple of pairs of loops either side of the backpack and along the suit legs and hips, then just slide poles into them to make the whole suit into a stretcher.