I have photos of any and all relevant documentation in a password locked folder on my phone, and I have hard copies of my permission slips hidden in my car.
I have avoided having hard copies of certs on me, other than when needed to purchase. Not worth the risk or faff of losing/damaging them. Even photocopies arent always a good idea and if lost or stolen, there is your address and a shopping list of your guns right next to it, but better than hard copies if no other option.
I think the best bet is photos on your phone protected by password or face ID