I figured it out. Premium features come when adding more than 3 subscriptions. When the Google prompt comes up, there is an option to add a code. The premium features, for now, are just adding more subscriptions. Hopefully, more to come!
For me, 'premium' signifies something extra, not a version of the app that allows you to fully use the core functionality. The 'free' version right now is more like a demo in that sense.
Having said that, the app really works well and the design is very nice as well!