1.
To upgrade form Windows 11 Home to Pro, with that licence key, you would usually need to backup your personal files, then clean install Windows 11 Pro from a bootable USB.

2.
Before you do that, try this method:

Important – disconnect totally from the Internet

Open the Settings App (Gear icon on your Starr Menu)

Go to Update and Security – Activation

Click Change Product key

Enter this generic product key: VK7JG-NPHTM-C97JM-9MPGT-3V66T

When prompted, click ‘Activate Product’

If the above does not work first time, restart your PC and try again.

Note the generic key will cause the Home edition to upgrade to the Pro edition, then you can enter your purchased Pro licence key in the Settings app after you restart (not shut down) your PC to activate the Pro edition.