Resolved. Mouse charged on a USB to Lightning (?) cable, at an independent charge station. Relinked to iMac desktop computer by plugging that cable in to computer USB outlet; checked charge status under Bluetooth, then Connected automatically while USB cable in. There was no visible indication on mouse (like a light) that the mouse was indeed charged. It did not link before physically plugging it into computer.
Tested the mouse for function, then removed manual old cable mouse I had been using while recharging. Always keep an old cable mouse around for working through such difficulties. The USB C and Lightning cables (what is a C cable, and what are they used for?) are mysteries to some of us older folks who have been using Macs since before they were "iMac." Ha.
Apple Support articles do not cover all permutations of devices and peripherals, and the recharge instructions were somewhat limited in definitions and photos of devices and cables. But did give me the idea that I needed to plug it to computer again, even if that was not shown in article.