I found that installing the full “gnome” package and restarting resolved the issue. I originally had gnome-shell, Nautilus, and Tracker packages installed by way of the Parrot GNOME Desktop meta-package, but something must have been missing that was needed for GNOME Shell search to communicate with Nautilus search provider and the tracker index. I have not figured out which specific packages affected the behavior.
Yes, I suspect the root cause is GNOME packages that are not really self-contained. Certain functionality requires multiple packages to interoperate, but it is not clear which sets or subsets are needed for certain functions. The work-around of bringing in the full GNOME Desktop Environment seems to be the best way to do it, even though it will lead to a number of installed packages that will go unused in some cases.