What does “The iTunes Store is unable to process purchases at this time” message mean and how can I fix it?

I had this problem for several weeks, starting in December 2020. I had four apps marked as having updates available. All of these failed with the error shown if I tried to update them. This is on an iPhone 4S running iOS 9.3.6.

Apple support suggested using two step security and registering a payment method, but these had no effect. Reset Network Settings had no effect. In Settings -> Privacy -> Location Services [on] -> System Services -> Setting Time Zone ON had no effect.

At this point I noticed that I could install a new app (different from all of the ones waiting updates).

Signing out and back in again to the App Store had no effect. Force restart had no effect. Factory Reset and restoring apps and data from iCloud had no effect.

WhatsApp was the app I was keenest to update (because they blocked the use of my previous version). I deinstalled WhatsApp. I installed WhatsApp. The first attempt no longer showed the “The iTunes Store is unable to process purchases at this time” message but failed in an obscure way. The second attempt worked!