I've activated automatic updates in Gnome Software Center. Now more and more updates are shown to me here. Even after a reboot, the update notifications are still there.
If I manually click on "update all" and reboot, the update notifications disappear, but I actually thought, after reading the documentation, that updates would require no action from me at all, and that's what I want.
The weird thing is, the installed programs themselves claim to already be on the new, updated version.
So why are the updates still shown in the Software Center?
Well for Firefox, the one getting updated is the native rpm version which is part of the standard Silverblue install while the one already updated is the flatpak version. The native version is just called 'Firefox' while the one from flatpak is called 'Firefox Web Browser' if I remember correctly. I have no idea why signal is showing up there. Maybe it is a bug.
Also next time a system update is shown in GNOME software, check using
rpm-ostree statusto see if any updated image is staged. If yes, then you don't have to bother with gnome software - when you shutdown or reboot, the update will automatically be applied.