what mac os for imac 27 inch late 2013 ?

that iMac can run up to macOS Catalina but no further. the download for Catalina can be found here >> How to get old versions of macOS - Apple Support

and note that as of Catalina, any 32 bit apps that you currently have will no longer work. you will either need to update them if a 32 bit version is available or replace them with comparable 64 bit apps.

jeffreythefrog wrote:

update them if a 32 bit version is available

correction: update them if a 64 bit version is available.