I purchased a cheap (£6) Windows 10 Professional key from an Amazon.co.uk marketplace seller to upgrade my Beelink AP34 from Home to Professional Edition.
When you try to activate your new professional license, it says it activated but the version stays the same. Some people then just do a full reinstall.
Sadly some sellers do not give the method required to activate without reinstallation, so here are the step required:
Before you activate with your new key, change your key to the following Microsoft Generic/Dummy Key:
This will cause the Home edition to download all the requirements for professional edition.
The computer will restart automatically and you will have an unactivated Windows 10 Professional, now active with your new professional key and you should have an activated Windows 10 Professional.