in the apple store i found apps macOS Ventura version and it's say what that apps working with compatibility to macOS 10.12 and later ! when i trying to download that apps the my iMac i see the message, Update not found !
When i trying to download apps from app store macOS Ventura version 13.5.1 to my iMac , i see massage "Update not found" the requested version of macOS is not available . But it's says what macOS Ventura version 13.5.1 has "Compatibility for macOS 10.12 or later" version . So my iMac has Catalina 10.15.7 version which is match your requirements! can you support with that .
iMac 21.5″, macOS 10.15