"Restart & Update" did nothing/failed silently
On my Fedora Silverblue 30 installation I have Google Chrome installed manually from the official RPM package through rpm-ostree. There seems to be an update for Chrome, and gnome-software offers a "Restart & Update" option to install it.
Unfortunately that did not seem to do anything. After restart I still have the old version of Chrome, and gnome-software offers the update again.