Thanks for these suggestions. I have tried rebooting the printer, and that doesn't appear to do anything. Oddly, however, I just discovered that when I turn it off, it ejects the attached hard drive that acts as the disk for my time machine. So there's clearly something odd going on there.
Nothing in the print queue, no software updates in the App Store, and no Windows partition either.
Switching from the USB hub to the iMac itself doesn't help either. Making that switch meant that the time machine didn't get ejected (it runs off the hub), but it did seem to make my UPS think that it had to start powering the computer.
So all of that suggests that it's some odd interaction between the printer and the new version of the OS, appearing to center somehow around the USB connection. So it's definitely a different problem than is otherwise being discussed here, and I'll probably need to put in a call to AppleCare.