You don't have to upgrade to Sonoma, but you should keep Monterey current. The Software Update panel will show macOS 14.4.1, but further down on that panel, you will see:
Another update is available.
More Info…
That More Info… link is to the current version of Monterey 12.7.4 (and probably Safari 17.4) that when selected, will install these, not Sonoma.
Before you make a decision to upgrade the operating system (e.g. Sonoma), you should determine if your printer/scanner vendor provides driver updates for Sonoma (macOS 14), or that the device is also supported without vendor drivers in Apple's built-in AirPrint service. You should also check any third-party applications for their support in Sonoma.
Ordinarily, you should not see persistent notifications to upgrade, but you will see a red badge icon on your System Preferences icon in the Dock.