My Mac will not update macOS Catalina 10.15.7

What is the model year of your iMac? The model year of an iMac is available at Apple menu > About This Mac.

A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. See: How to download and install macOS - Apple Support

A mid 2014 and late 2014 iMac can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to download and install macOS - Apple Support

A late 2015 iMac can be upgraded to the latest version of Monterey macOS 12 but no later. See: How to download and install macOS - Apple Support

A 2017 iMac can be upgraded to the latest version of Ventura macOS 13 but no later. See: How to download and install macOS - Apple Support  

A 2019 or later iMac can be upgraded to the current version of Sonoma macOS 14. See:How to upgrade to macOS Sonoma - Apple Support

Sorry - Catalina 10.15.7 is the highest possible for a late 2013.

Also see the following from Identify your iMac model - Apple Support

iMac (27-inch, Late 2013)

Model Identifier: iMac14,2

Part Number: ME086xx/A, ME088xx/A

Newest compatible operating system: macOS Catalina

iMac (21.5-inch, Late 2013)

Model Identifier: iMac14,1

Part Number: ME086xx/A, ME087xx/A

Newest compatible operating system: macOS Catalina

Go to Apple > About this Mac and tell us what model and year the Mac is.