How do I authorize my Mac mini Pro for my itunes

See the "How to authorize or deauthorize your Mac" section of Authorize or deauthorize your computer for iTunes Store purchases - Apple Support

Note that the instructions specify to use the Music app or the TV app, since the iTunes app for Macs was discontinued. The iTunes app for Mac computers was discontinued and replaced when macOS Catalina was released. It cannot be installed on Macs that are running Catalina or later. See the following Apple article for information about the replacement apps: What happened to iTunes? - Apple Support

Did you sign into the iTunes account in the Music App (Account menu)?