Epiphany (Web) is crashing on extensions.gnome.org where it wasn't previously, but that's the only issue I've discovered and is fine to be tracked separately. https://bugzilla.redhat.com/show_bug.cgi?id=1206568
So, it took a lot of debugging today, but it turned out that I got unlucky and hit a separate bug at the same time. I have a third-party repo in the mix that changed signing keys yesterday. PackageKit didn't handle that gracefully, which caused this to continue to fail, even though this fixed the original bug. Changing my karma to +1.
So, I'm told that I needed to reboot before this would work. So I rebooted. It continued to not work. I tried removing /var/cache/PackageKit/* and refreshing the Gnome Software updates tab. That also did not work. It appears that once we are in this situation, something is well and truly broken.