This error usually means Windows thinks the hardware changed after the BIOS update. If the motherboard itself wasn't replaced, try Settings > System > Activation > Troubleshoot first. If your digital license is linked to your Microsoft account, choose “I changed hardware on this device recently” and follow the steps to reactivate it.
I wouldn't buy another key yet. If the troubleshooter doesn't work, check that the installed edition is still Windows 11 Home and that you're signed into the same Microsoft account that was previously used for activation.