"could not sign in" App Store on iPad

My iPad won't allow me to sign in to the App Store. I enter my credentials, it spins for a moment like it's going to sign in, and then "Could Not Sign In" appears with nothing else. No errors or anything.

Background - upgraded the iOS today to 12.4.7 (latest allowed for my model apparently). When I went to the App Store and tried to re-download some previously deleted apps, it just said it would download them, but nothing would happen. Tried rebooting, no joy. Tried a reset (power button and home button), no joy. Logged out of the App Store. When I tried to sign back in, it gave me that message. Tried resetting my password, just in case. That successfully resset and the iPad prompted me for my new credentials, but the App Store still won't sign in. I'm on WiFi and I can do all sorts of other tasks on the device that use the network. Just no sign in to the App Store!