I have EXACT same issue as your iPhone 12 pro. Bought via Apple.com directly for store-pick up (sim-free version).
Contacted Apple Specialist tech support via chat, and all they could say was just wait for the next iOS update for a fix...
On the other hand, other online forums have rumors saying it can possibly be hardware issue rather (ie. defective OLED screen from such and such manufacturer). Not sure what to believe, but at this rate, I think there CAN be issue with not being able to light up on/off properly from hardware perspective... (sure, apple can come up with software patch that can remedy the issue within native apps/interfaces, but what about 3rd party apps/interfaces? If it's truly hardware issue, then the issue will most likely persist even after such n' such iOS update...*)
Let's hope for miracle. At least for me, I still have the extended holiday return window, so I can wait it out a bit... but for others who can't qualify for it, I still definitely feel the pain... (am doing hardware reset like, every other day in hopes that it can glitch out of it or something during restoring process IF it's indeed rogue software bug...)