Hi, good day!
Since the Windows Update problem started after changing the product key, could you first check Settings > System > Activation and let me know what it shows under Activation status?
Also, please press Windows key + R to open Run, type winver, and let me know the Windows 11 version and build.
If Windows shows as activated, please also tell me the exact error message or error code you receive when Windows Update fails.
I look forward to your update and am willing to collaborate with you until we resolve the issue. Keep me posted by clicking "Add comment" below.