Sure.
So, I wrote about problems I had with populating, and another user came up with this solution.
As long as the type of my API key is set to «Read-Only» the relations will never show up, regardless of how I format my request (e.g. populate=* or populate[0]=authors&populate[1]=categories). Also this solution for deeply populating objects does not work. The only solution currently seems to be changing the token type to «Full access» .