Is there an upgrade to High Sierra above 10.13.6? I cannot run a more advanced version of Photoshop 2020 or 2021 on this system

So your iMac is able to run the latest macOS version - macOS 12 Monterey.

I am not an expert on Adobe apps, so I am not sure what the compatibility of those apps is with the various macOS versions throughout the years. It depends on the Photoshop version (2020-2021 will run on Monterey)

If you wish to upgrade macOS, here is a link on how to go to macOS 12: https://support.apple.com/en-us/HT212735

There isn't an upgrade to High Sierra past 10.13.6, but depending on what Mac you have, you can upgrade past High Sierra to a newer macOS version. What model Mac do you own (click the Apple logo >> About this Mac).

*Note that if you have Adobe CS6, you cannot run them on macOS 10.15 Catalina and up since these versions don't support 32 bit applications.

👍

Sorry, I should've elaborated, what year is your iMac from?