I'm now on 13.5.1 and have exactly the same issue - the lock button doesn't work after taking a screenshot. Sometimes it rights itself, other time, I have to power down the phone and restart. It's very frustrating.
Spoke to Apple chat, they suggested wiping the phone, which I did, however, the same problem occurred even before I'd reinstalled it from a backup.
Now I have to take the phone in to the Apple store. Really not happy as I've had the phone less than a month and I'm guessing they'll want to keep it for a few days and I'll be left phoneless!
The support via chat was pretty useless, they didn't really add anything that I hadn't already tried and I managed to encrypt my backup with an unknown password (my fault!) so I lost about 3 weeks of data into the bargain.