I think that most facial recognition software looks at eyes, cheeks, and chins to determine matchings. However, Apple did revamp their phone unlocking app to be able to work even if one is wearing a surgical mask.
I'm surprised he hasn't tried the doggy door over to the left.
I have to drop in the door cover on our doggy door every night on ours to keep the 'coons out. Several years ago, it was time for bed, one was in our sunroom, likely hiding under the rattan loveseat. I dropped it in, went to bed. Panicked, he managed to force his way out the screen door, shredding the weatherstripping at the bottom of the door.
I replaced the weatherstripping but now I look under the loveseat, 2 chairs and 2 tables with a flashlight before dropping in the door cover to the doggy door.