Bizarrely, my unsupported app, which produced the error message 'this app needs to be updated to work with iOS 14.5' has now started working under the same OS! (And without any change to the app.)
All I did was to erase the iPhone, then restore it from an iCloud backup from just before the upgrade to 14.5. During the restore process, the phone kept upgrading the OS to 14.5 and I couldn't find a way to stop it, despite trying the process three times.
I then gave up, erased the phone again in case I had introduced problems by tampering, then restored from a backup made after the OS upgrade. When this had completed fully, I tried the app again and it opened properly.
My problem is solved (I don't know how or why) and I report the story in case it's any help to anyone else. Good luck.