Here’s the history:
(1) The “App Store” icon displayed a “1” encircled on its upper right hand corner.
(2) Opening “Updates” shows that an update awaits for “App Store.” No other apps; just this one!
(3) I click to initiate the update; the progress clock starts in motion, and when it completes, the “App Store” app reverts to inviting me to again “update” the app… this continues ad nauseam!
(4) When King_Penguin (above) informed me that another icon, “Apple Store,” likely existed on my iPhone, I searched, and indeed, it was found… but there was no indication that it required an update!
(5) However… following his advice, I deleted the “Apple Store” app… and, with that action, the “Updates” page no longer informed me that the “App Store” app required updating!
Believe it or not! 😟