Hi Imago. I'm Greg, an installation specialist and 9 year Windows MVP, here to help you.
If this the WIndows 10 Product Key on an official COA sticker which has the licensed version on it so you know which version (Home or Pro) it will work on? Do you know for sure you installed the correct version?
Have you tried inserting the Product Key into Settings > Update & Security > Activation > Change Product Key. What does it report on the Activation settings page under Status and Edition?
I hope this helps. Feel free to ask back any questions and let us know how it goes. I will keep working with you until it's resolved.