I believe you can change product key from windows 11 home to pro with a computer with a windows 10 pro product key
Press Windows key + X.
Click Command Prompt (Admin)/ [PowerShell if you feel spicy].
At the terminal window, type the following to reveal the product key feel free to copy/paste it! without the arrow:
→wmic path SoftwareLicensingService get OA3xOriginalProductKey
this will show you your product key in (XXXXX-XXXXX-XXXXX-XXXXX-XXXXX) format
my reference: How to Find Your Windows 10 Product Key (groovypost.com)
feel free to correct me if i am wrong. (in which I probably am