Why won't my iMac (27-inch, Late 2013) update past Catalina 10.15.7?

Sorry, my friend. Your iMac won’t upgrade beyond Catalina because it cannot. There is no upgrade path for that hardware.

If you wish to use a newer macOS then you will have to buy a new or newer Mac.

For it’s worth I’m also stuck on Catalina on my late 2013 27 inch iMac. I am patiently waiting for the hoped for arrival of a new, larger M1 iMac. So are lots of us 2013 owners.

I love my own 27" 2013 Catalina-limited iMac.

Like you and many others, I'm eagerly awaiting an M1 replacement model.

👍🏽