What OS will run on an iMac (21.5-inch, Late 2015)?

A late 2015 iMac can be upgraded to the latest version of Monterey macOS 12. See:How to download and install macOS - Apple Support

Also see:

Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.stclairsoft.com/Go64/

or

 https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html

and

https://helpx.adobe.com/x-productkb/global/fix-macos-64-bit-compatibility-errors.html

Back up your data, check the application compatibility table, click here, and then on the download link for a higher OS; that model's maximum one is Monterey.

Catalina and above won't run 32-bit software; if you choose one of them, use Go64 as well.

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stinams wrote:

I need to update my late 2015 iMac OS. Certain browsers are no longer supported and I'm stuck. I can't upgrade to the latest OS, but I thought I was able to upgrade to High Sierra or another. I assume I'm going to lose all adobe programs. What a shame. So much greed. The machine is still perfect, but adobe is a whole other issue. I'm running El Capitan. I know. I know.

Adobe generally requires one of the "most recent three".

Apple hasn't announced when Sonoma's successor will come out, but if recent history is any clue, it will come out about a year from now. If you upgrade to Monterey now, you'll have about a year during which your late 2015 iMac will be running one of the "most recent three".

Note that Photoshop CS6 and Lightroom 6.14 contain installation and activation code that won't run under Catalina or later, so you would need to move to "subscription" versions of Photoshop and Lightroom Classic. I believe there is a Photography Plan that includes access to PS, LR, and LR Classic for $10/month.