Why Big Sur is support on 2013 MacBook Air, but not support on 2013 iMac?

We are fellow users and cannot answer why questions involving internal Apple product support decisions. Most likely reason is that the Late-2013 does not provide the Metal graphics support that is required by Big Sur.

You can only upgrade as far as Catalina, and that brings new issues about only supporting 64-bit applications. My Late-2013 iMac has Mojave 10.14.6 installed, and that is as far as I plan to go with it. Sits right next to my M1 mini and 32 inch 4K display.

Any consolation - iMac Late 2012 here and Catalina End of the Road. Waiting to M1 / M2 iMac whenever that happens.