Mac mini won’t update with compatible updates

Back up your data, check the application compatibility table, click here, and then on the download link for it. Intermediate macOS versions won't show up in a search and can only be accessed through direct ones.

Catalina and higher won't run 32-bit software; if you upgrade to one of them, use Go64 as well.

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Follow the steps at > Update macOS on Mac - Apple Support

If that doesn't help, then see > How to download macOS - Apple Support

Also if you have downloaded a macOS Installer from the Mac App Store, then you need to check in your Applications Folder for the macOS Installer.