There doesn’t seem to be a way to customize the Touch Bar for iTunes/Music. Not all apps support customization.
In many apps, like Finder, Mail, and Safari, you can customize the Touch Bar.
Choose View > Customize Touch Bar. The customization window appears on your display, allowing you to choose your favorite items
Note how they say “many” instead of “all” and don’t mention iTunes. Also notice the specific instructions given for customizing the Touch Bar - implying that an app made directly by Apple wouldn’t have a roundabout way of configuring the customization.