Software Update Problem

iMac late 2013 tops out at macOS 10.15; Catalina.

The link to the Catalina download is included here: How to get old versions of macOS - Apple Support

Have a backup prior to upgrade.

Confirm all apps and all printer and scanner drivers are all 64-bit. You can use the Go64 tool to find the older 32-bit apps which will not work, and which will need a replacement or retirement or update.

The alternatives include migrating to and using Apple iWork Pages, Numbers, and Keynote, and which are free, and which can read and write many Office documents, or acquiring an alternative suite such as LibreOffice, which is free.

With the impending arrival of macOS Ventura, Catalina will be out of the newest three versions, which usually means Microsoft support for Catalina will be ending soon.

Apple differentiates updates (what you are checking) from upgrades. Updates are minor changes and fixes and are expected to be compatible changes. Upgrades are larger and more involved, and can and variously do disrupt some apps, and can add or remove various features. Upgrades must be specifically requested, as app stuff can break.

Please post the model year of this iMac. The iMac model and model year are displayed by 🍎 > About This Mac. With the model year re-posted here, we can provide you with the available upgrades options.

Examples: iMac (Late 2012 or newer) can get to macOS Mojave, and iMac Late 2015 can get to macOS Monterey, for instance. Macs older than these will top out at High Sierra, or earlier.

Or you can learn more about this upgrade yourself: How to get old versions of macOS - Apple Support

Have a complete and current backup before performing any upgrade.

There can be other upgrade considerations, depending on which macOS version you (can and do) upgrade to.