Knock on wood ... this has not happened to me (...yet). But I did a bit of investigating on my own iMac today (Intel i9, Monterey 12.7.2).
I have two accounts, both admin, let's call them A and B. The A account is the first one created when I installed the iMac and is where I do all my truly system admin work (installs, updates, etc.)
In the A account, when I checked Software Update the only option I had enabled was Check for Updates. I disabled (unchecked) Check for Updates, the text greyed out, I clicked OK and no longer had any indication of any available updates, Sonoma or otherwise. Also, the System Preferences icon on my Dock lost its little red indicator showing any updates available.
Rebooted the iMac, logged back into account A, there was no red indicator on System Preferences; I opened Software Update, there was no text or graphics whatsoever about any updates. It was clearly not checking anything. Cool, I thought.
Then I logged out of account A and logged into account B. Lo and behold the System Preferences icon on that Dock had its little red indicator showing, as did the Software Update icon in System Preferences. When I opened Software Update I found that both Check for Updates and Download new updates when available were both checked. (I had probably not unchecked them previously.) I unchecked both ... and this time the text for Check for Updates remained black (it did not grey out even though it was unchecked). I went in & out of this a few times and despite disabling Check for Updates the system checks anyway.
I then logged out of account B and went back to account A. NOW, even in account A, although Check for Updates is unchecked, the text is also black (not grey) and the system checks for updates regardless. I suspect the black text is an indicator that checking for updates is actually still enabled. (I also shut down & restarted to see if that made any difference; it did not.)
So, clearly something is amiss in the system's settings (at a minimum regarding Check for Updates).
Among other things, it proved to me that each user account has its own full set of preferences. And it would appear that if you have multiple user accounts on a Mac you should make sure to disable Software Update in all accounts.