Error 0xC004F034 indicates that "The license was not found or could not be used" due to "The user is trying to activate the PC by the KMS server or the key does not match". Unfortunately, the seller deceived you by selling the stolen key, not the ESD license. Microsoft warns of similar cases:
"If you see a listing on an auction site, online classified ad, or other online page advertising product keys for sale, it’s a good indication that the keys are likely stolen or counterfeit.
If you were to purchase and use a stolen or counterfeit product key to activate Windows installed on your PC, the key may not work for activation, may already be in use on another PC, or it might be blocked from use later by Microsoft when the key is reported stolen...."
https://www.microsoft.com/en-us/howtotell/shop
A genuine Windows 10/11 Professional edition license costs about 200 USD. Compare with the cost of the "key". I recommend contacting the seller and requesting a refund. And also, in the future, do not buy "keys" on keysfan and similar pirated resources.
Download the Show Key Plus utility: https://apps.microsoft.com/detail/9pkvzcprx9nv?...
and run it. On the homepage, check if there is a 25 digit key in the "OEM key" section. If there is, then that's good (the laptop has a factory license). In this case, you can solve the problem by installing the correct version of the OS (activation will take place automatically). If there is no OEM key, then you need to purchase a license (not a "key") for the standalone (BOX or ESD) version of Windows and perform a clean install with activation with a genuine key from the license purchase kit.