Thank you Giulio. I'm not new to tech and I've dealt with too many others whose reply is typically, "Try turning it off and back on, again." I become rather sensitive, if not defensive to such ultra-basic advice. Yours was a fair question and an elaboration on the things I tried does make sense for people offering assistance. I'd not put specific trouble-shooting steps tried in my original post.
I just used the same cable in an Apple wall adapter. It started charging normally. Green battery icon, lightning bolt icon beside it, and no error message. Using the very same cable again, I replugged in to my iMac. The error message came up in about 6 seconds. That rules out the cable. However, your wall plug power adapter trouble-shooting suggestion caused me to try something else.
I plugged in to a USB port on the back of the iMac itself. Prior attempts were from a powered USB hub because I have too many USB devices for the limited number of ports on the iMac. The error did NOT reoccur.
On closer inspection of the USB Hub, it appeared that the 3V DC power adapter had pulled out of the hub. All power used by the hub was being supplied by a USB port from the iMac. That low power is split between four total devices, including the iPhone. After re-"powering" the hub (simply restoring the adapter plug into the jack), I tried the iPhone USB cord in the hub. The error did NOT reoccur.
The iPhone seems to now be charging as expected with no error, plugged into the USB hub, as long as it has external power.
Thank you for giving ideas for further trouble-shooting. There is still a puzzle, though not quite as annoying as before. Prior to the iOS update, the iPhone powered fine in the [unpowered] USB hub. After the update it did not. Restoring adapter supplied power to the hub caused it to charge normally. Somehow, whether in the recent iMac operating system update, or the iOS iPhone update, slightly more power is now required for iPhone charging. Not the same amount as required by an iPad, but more than the unpowered hub was able to provide.
Now that I know this new power requirement, I have no further concerns or issues (at least not yet!).
Thanks, again for the suggestion to keep trouble-shooting, and the inspiration to dig further into the problem.