Hi Tobias,
I am Sumit, an Independent Advisor and a 3 year Windows Insider MVP here to help.
As of now, do you have Windows 10 Home?
Technically how activation works is - the Pro upgrade inherits its type of license from the qualifying edition, which is Windows 10 Home OEM license in your case. OEM licenses are generally non-transferable to other PCs.
Contacting Microsoft Support on Monday is the recommended course of action so that they may issue you a new license. I have a way to upgrade Home to Pro, but the thing is if you are unable to activate and is my above statement goes true, you would be left with an unactivated OS.
Please use the contact us link here:
https://support.microsoft.com/en-us/contactus
Type "talk to an agent" in the Virtual agent and choose Windows/ subcategory.
You would be presented with a link of options which are available for your country - call me back, Chat or call.
Additionally, country-wise phone numbers are given here: