Today's hardware usually no longer has a licence key printed on it. However, you can read this out by entering the following command in Windows Powershell:
wmic path SoftwareLicensingService get OA3xOriginalProductKey

I bought this computer and did not have to enter a licence key to initialise it. Passwords were required for start-up or to return from standby. Microsoft updates run smoothly afterwards.

... I think so too. As far as I know, licence keys are no longer needed for operating systems (unlike program packages such as Office, etc.).

The key is no longer on the device and no longer appears in the system settings. But in practice you don't need it any more. You can update Windows without any problem.