There are masks and pillows specifically designed for stomach sleepers. But stomach sleeping is somewhat uncommon, and plenty of people who sleep in more conventional positions can't adapt to sleeping with a CPAP, so you probably just have to find out yourself.

FWIW, I have sleep apnea and I'm a strict side sleeper. I also had a real tough time getting used to sleeping with something attached to my face. Sometimes I still take it off if I'm awake too long during the 2-4am time period, but most nights I sleep through without even noticing. I use a nasal mask, though, I absolutely have not ever been able to tolerate a full face mask.

Definitely doesn't only affect back sleepers. I sleep almost exclusively on my side. There are some very small masks including a type that only has two tiny "pillows" (as I understand they are called) that rest right up on/in your nostrils. Mine basically only covers my nose and has the hose on the top of my head so I can turn from side to side. I'm not sure that would be good enough for a stomach sleeper, but it might. I can see how being a stomach sleeper could make wearing a respiratory mask difficult, for sure.

I was a stomach sleeper before getting a CPAP. In retrospect, I was a stomach sleeper because my body figured out it made breathing easier. Rarely find myself sleeping on my stomach any more.