Hi Ursine,
Thank you for posting, I am here to help you today. A blank output after running wmic path SoftwareLicensingService get OA3xOriginalProductKey. Possible that product key is not stored in your Computer BIOS.
Aside from Powershell try this command using Run command with administrator access. Then type this command
wmic path SoftwareLicensingService get OA3xOriginalProductKey see if it still getting blank.
Please check also your activation settings see if its is showing Windows is activated with a digital license? If so, your OS is activated without a product key, so there is no key stored on the system to retrieve.
For more information you can check this article:
Find your Windows product key
I hope you find this information helpful. Please let us know if you have any further questions If the answer is helpful, please click "Accept Answer".
Best regards,
Jansher