...
I thought about it some more, I have the App Store notifications set to off, maybe that's what sends the notifications about updates to the OS?
App Store updates do not control system software updates.
If your Mac is Apple Silicon (Apple M1 processor, not Intel), then I think that Power Nap is not a user accessible setting.
After some searching, I think that the notifications are set only by the Software Update pref pane.
Try toggling those settings:
Software Update pane/Advanced. Turn OFF (uncheck) "Check for Updates" You have to authenticate to turn that off.
That should result in ALL boxes being unchecked - including the "Automatically keep my Mac up to date" on the main window.
Quit System Preferences. I would probably restart my Mac at this point, that's up to you...
Re-open System Preferences, then Software Update, and
click that "Automatically keep my Mac up to date"
Check in Advanced - all boxes should be checked now.
Uncheck the Download new updates when available. That will uncheck the two boxes below that automatically, and will uncheck the "Automatically keep (etc)" box on the main window, too.
(I would also suggest that the tip from bogdanw about deleting the preference files related to Software Updates would be a good next step, before trying the simple off then on toggle that I offered! )
If you begin getting notifications of new updates after using that modified setting/reset that I suggested, then you should be able to turn the "fully automatic updates" back on - those should then be working for you.