For some reason, the headers for 5.4.0-42 weren't installed by apt automatically. (I did the original offending kernel update as part of a prompt from the "Software Updater" GUI.)
Installing the headers with:
sudo apt install linux-headers-5.4.0-42-generic
caused apt to automatically recompile the nvidia kernel module for the new kernel. After a reboot to the new kernel, everything just worked.
I'm not sure why headers weren't installed automatically (I believe they usually are?). Perhaps there is a problem with the apt package for the new kernel? (It was released 2 days ago as of this post.)
This happened on the 20.04 Focal release.
Update:
Per the comments below, the linux-headers-generic metapackage (and the linux-generic metapackage) was not installed on my system. It looks like they were removed on the day that I upgraded to Focal. It happened around the time of removing an old Nvidia driver.