I am unable to update my safari on my desktop MAC. Has anyone else had this problem?

The Safari browser sometimes gets its own update, but typically is updated with a macOS update or upgrade. Of course, that only happens if your Mac can support the newer macOS version. But you may not actually have to upgrade the macOS to get your website access back.

If you are having trouble connecting to and using websites with your older version of Safari, try it with a newer third party browser that is still being updated to meet current internet security protocols.

I suggest you take a look at Firefox browser or Brave browser.

Download an alternative browser and install it into your Applications folder. Launch and use that when you encounter websites that don't play well with Safari.

Safari is considered part of Mac OS, that means in order to get a later version of Safari you must update Mac OS. If your model year iMac cannot be updated to more current versions of Mac OS then you must try other browsers or perhaps it is time to replace the Mac.