Whew! I knew that rebooting does not stop and restart the wi-fi radio, but shutting down and restarting the machine does. It just occurred to me that doing a shutdown and restart rather than a reboot might get my laptop working again.
It did.
When it started up again, it was connected normally. I'm going to go ahead with the rest of these updates, and shut down/restart if rebooting fails for them too.
EDIT: Note that I've never needed to do that before this update. Normally a simple reboot has always worked without any drama.
MORE EDIT: The problem may be DE-specific. I just rebooted the Budgie laptop without a problem. Going to try the multimedia machine now, another Plasma machine.
AND EVEN MORE: The update and reboot worked without a problem on that computer, which is another Plasma machine. So no DE-specific problem, apparently. I'm going to assume this was an example of "shit happens," and not worry about it any further. There must be something about this particular laptop that caused it to require a shut-down instead of a reboot. Never happened before, though.