I had a problem reinstalling Win 11 on my Mini S 11th gen until I double checked and discovered I was trying to install the wrong version of Win 11. Once I reinstalled Win 11 Pro, it activated just fine without needing the key.
Everybody, make sure you’re reinstalling the version of Win 11 that came installed on the machine when you got it. The key is matched to the BIOS and it needs the correct version.