latest OS for iMAC 27" late 2013?

Catalina is already out of support. Typically, Apple only supports the current version and the 2 previous versions.

They may release a security update here and there if it's deemed critical enough, but officially support for Catalina ended when Ventura was released.

Catalina is the latest version of macOS that a 27" Late 2013 iMac can run, but it's not the only version available.

MacTracker says that machine came with assorted versions of Mountain Lion and Mavericks. There are several older versions of macOS that you still can get, and that you could install (using a "clean install" on a spare drive). The main one of interest would be Mojave (10.14) – if you had some 32-bit applications you wanted to resurrect. Otherwise it's best not to downgrade, and to stick with Catalina.

Catalina is correct.

Buy a new Mac. That one is 10 years old. It is obsolete.

Thank you so Much waiting for the New 27 inch iMac not a 24 inch. and Salute, Thank You For Your Service. Me 73 to 93 usaf. Looking at Mac Mini with M2 Pro