Power BI Service API not available in Azure Portal

Hi. I have registered my first demo app through the Azure Portal. (I also tried registering the app using the PowerBI App Registration Tool, but that gave me an error: "You aren't authorized to register applications. It's possible your tenant administrator has authorized only admin users to register applications. Please contact your administrator.") Anyway, I got passed that using the Azure Portal so thats fine. 

Now I am encountering a second problem. At 'Required Permissions' I do not have Power BI Service (Power BI) available. There is a note on this issue at the register-app help page (link) saying 

If you created the app directly in the Azure AD portal, Power BI Service (Power BI) may not be present. If it isn't, select + Add and then 1 Select and API. Select Power BI Service in the API list and select Select.If Power BI Service (Power BI) isn't available within + Add, sign up for Power BI with at least one user.

The latter applies to me. Power BI is not available within + Add, so the note says I have to sign up for Power BI with at least one user. But i dont understand this, since I am signed up to Power BI and I am logged in. (The top right corner clearly displays my name and email and says I am logged in). 

I am clearly misunderstanding something. What do I have to do?

Many thanks for your help!