Still getting Upgraded for Mojave on 2013 iMac

The 2013 iMac cannot be upgraded beyond Catalina 10.15.7 plus security updates. And now that Catalina is an unsupported Apple operating system, it is unlikely (but not impossible) that it will receive future Software Update notifications about security updates.

If you are currently running Mojave, then Software Update will show Catalina 10.15.7 available for installation.

If you are getting a notification about upgrading to Monterey, you might. I have two Macs that can't be upgraded beyond Big Sur yet I still get a Monterey notification. I never have figured out how to stop it.