Problem solved. Or, more like, solution blundered into.
Originally I didn't think I could log in because I wasn't familiar with the Mini 6 gestures to make the PIN keypad visible. I then tried to Shut Down, but it didn't seem to be responding to the Power Button + Volume Button protocol, but maybe I just couldn't see the power off slider because of the partial screens. Eventually I found I could make the PIN keypad visible and log in, and from there the iPad could be forced to shutdown via Settings > General > Shut Down. After it booted up everything was fine.
After ten years of using the Mini 1 and Mini 5, the controls on my wife's Mini 6 drive me crazy. I have no idea the advantage of having no physical power button on the Mini 6 screen is. Must be something really good, I hope.
![Unamused face :unamused: 😒](https://cdn.jsdelivr.net/joypixels/assets/6.6/png/unicode/64/1f612.png)