If you are using the automated setup, you will fail every time with a Pro key (at least from my experience). The automated setup I believe defaults to Home. My best "guess" is if you are using an OEM key, those are suppose to be tied to hardware purchases. Microsoft really enjoys making licensing software frustrating.
The only way to get it to work is do a custom installation, and during the installation select Windows 11 Pro.
I don't know if this is an ARM thing or a "Microsoft being Microsoft" thing. I could have sworn at least at first it was relatively easy to switch simply by just putting in your Pro key, it would restart, and everything would be good.