what operating system should I be using on my iMac (27-inch, Late 2013)

Personally, I would use the latest possible - Catalina.

A late late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. See: How to download and install macOS - Apple Support

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

Or abandon Apple 32-bit applications such as the iWork '09 and earlier suites, iPhoto, iMovie '09, Aperture, etc.