The iTunes application was discontinued with macOS 10.15 Catalina in 2019 . You cannot get the iTunes application on a Mac running Catalina or higher at all, which includes Ventura and the current Sonoma.
The only option is to use the Apple Music App. You do not need a subscription to use the Apple Music app.
With that said, how exactly was your library stored in iCloud?
iTunes does not store music in iCloud unless you are subscribed to either Apple Music or iTunes Match.
If you are subscribed to iTunes Match, then it can work with the Apple Music app just fine, and access your library.
To do this, you need to turn on the Sync Library option in the Apple Music app.
click here ➜ Use Sync Library with your Apple Music or iTunes Match subscription - Apple Support
If you are not subscribed to either of the services, then the iTunes or Apple Music apps simply do not store music in iCloud and cannot access music from there directly.
If you explain exactly what it is you did to store the music on iCloud someone may be able to advise.