1
If there is a PC manufacturers OEM licence stored on the motherboard, then Windows should activate automatically after you re-install Windows, without the need for a product key.
Are you sure you have re-installed the exact same edition (Home or Pro) of Windows 11 that was previously installed on the PC?
2
Download the free ShowKeyPlus app from the Microsoft Store.
Please provide a screenshot of that app window and please hide your product key in the screenshot.