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?
Those might be flatpak "refreshes", which show up as "updating to the same version". As described by a flatpak maintainer, sometimes an app or runtime gets updated without changing the user-facing version number. I assume that's what you're seeing here.
the version change is right there in the screenshot.
The screenshot doesn't show any version change to signal - the version number is the same, so I was just answering why you might see an update like that since I thought that was part of your question.