Hi,
If you have the product key but Windows didn't activate after the BIOS update, you can wait a while to see if it activates automatically. If it doesn't...
You can try activating it using the hardware change process at the link below:
https://support.microsoft.com/en-us/windows/activation/reactivating-windows-after-a-hardware-change
If that doesn't work, try manual activation. First, note down your key using ShowKeyPlus: https://apps.microsoft.com/detail/9pkvzcprx9nv?hl=en-US&gl=US (install and open the app to find your key).
After noting down the key, disconnect your PC from the internet, open the Command Prompt as administrator, and run the command: slmgr /upk (this uninstalls the current key). Then, run the command: sfc /scannow, wait for the process to finish, and restart the computer.
After restarting the PC (and keeping it offline), go to Start > Settings > System > Activation > Change product key, and enter your key to activate. If recognized, Windows will activate; then you can reconnect to the internet.
Let me know if it worked.
Thanks.