I’ve not seen reports of this bug and I’ve never experienced it. I’ve run basically every beta since iOS 13, had every generation since the iPhone 7, and I have my own iPads plus all of my kid’s iPads across a couple of generations and I’ve never experienced it disconnecting when the screen becomes locked.
I’ve had it where they couldn’t see the network if I lock before they’ve connected, but once they’ve connected I’ve never seen disconnects just because the screen is locked.
I would be royally irritated if I did experience it though. Have you tried erasing everything and setting the phone up as new and hotspotting? Maybe there’s a small bug somewhere in your backup causing the issue that a restore carries over?