I feel your pain. I really do.
Looking at your screenshot, I also see "Snap package updates are checked routinely and installed automatically." How nice. So, in addition to Gnome Software Updater ignoring your preferences... It also notes that where Snap is concerned, you don't even get to state your preferences to have them ignored.
Maybe it is because it is now 2:35 am. And been a tough day. Maybe it's just me.
- Gnome-software: Buggy. Barely works. Constantly needs to be fixed. Complaints about it are all over the web.
- Gnome-extensions: Conflict, crash, freeze, cause conflicts with other gnome packages for no apparent reason and must be reinstalled. They corrupt out of the blue and the only reason that they exist at all is because Gnome keeps removing essential features.
- Software & Updates: Directly integrated into Gnome-Software and just as glitchy.
- GDM3: Corrupts out of the blue. Has to be reinstalled repeatedly. Allows little in the way of user configuration. Hard to navigate, details are hidden including the Gear Icon to change the desktop at login. On this forum I must constantly help people try to find the thing. So integrated in, that any issue with it breaks multiple essential services.
Don't even get me started on Gnome trying to pull out of the Gnu General License in order to assert more control over the user without the Gnu License inhibiting them. Much less that is going to get much worse with Gnome 40 (gtk4) since that removes a lot of essential classes from the toolkit, undercutting everyone that uses the gtk toolkit, for the primary reason of asserting Gnome Dominance over all other desktop environments.
Microsoft is less controlling and domineering than Gnome.
And somehow... Gnome is the Most used Desktop Environment on Linux. Its tendrils are into everything...
The problem you are having is Gnome. Gnome is asserting its control.
And the only fix I know of is to disable Gnome Software Updater.
I apologize... I am past it... the diplomacy and trying to walk on eggshells about GNOME. The only fix for all of the Problems with Gnome is for everyone to Stop Using It.
I'm out for the night.