Hi,
In addition to @Bence Weiszmann ence's procedure, if you purchased the Pro edition from the Microsoft Store and it still didn't update to the Pro version or gave an error:
First, install ShowKeyPlus and note down your Windows 11 Home product key:
https://apps.microsoft.com/detail/9pkvzcprx9nv?hl=en-US&gl=US
After noting down the key, disconnect your PC from the internet.
Go to Start > Settings > System > Activation.
Select "Change product key."
Enter the generic key: VK7JG-NPHTM-C97JM-9MPGT-3V66T. It will ask if you want to upgrade the edition; select "Yes" and wait for the process to complete.
Once it finishes and updates to the Pro version, you will need to open the Command Prompt (as administrator) and run the command slmgr /upk to remove the generic key; you should receive a notification that the key has been uninstalled.
Reconnect your PC to the internet, then go to Start > Settings > System > Activation > Troubleshoot. It will attempt to detect the upgrade you purchased via your Microsoft Store account.
Please consider rating the question (accept the answer or not), and access the community at Microsoft Q&A if you have further questions.
Thanks.