Thanks for that link!
Oh man, that is a confusing thing for sure! This should be written in big red letters all over the documentation, because, yes, I had made the same mistake.
So for everybody also struggling. Just look again at what sections are and what they’re for.
To complete the bewilderment: The fields section can have a files field; you’d want that, if you want to query files from other places. Otherwise rely on the files section, thru which you can upload files as well – and have the template set correctly.
Thanks again so much, @kinkwilde!