Firmware update alone doesn't trigger a reboot when "reboot and update" is clicked.
Please describe the issue you’re experiencing: When Gnome Software has a firmware update, and no other updates, the "Update and Reboot" button does not trigger a reboot (Thought when next rebooting the firmware update is performed)... this could be dangerous as the user might have forgotten that a firmware update is queued, and it could result in them doing it when they are not in a good situation for reliable power etc.
What Linux distribution are you using, and what kind of package (RPM, deb, flatpak, etc.) are you experiencing the problem with? I'm actually seeing this on Ubuntu 23.04, but it has the upstream (Not Canonical) "Gnome Software", as well as Flatpak tools installed... I can't replicate the issue on other machines, etc. because they don't have regular firmware updates.