W11 Pro OEM not activating - also no key in the envelope

I've bought a Windows 11 Professional OEM. For reasons unknown to myself I could not start the installation from the DVD, meaning it didn't boot from the DVD. So I re-inserted my HDD with Windows 10 on it and installed it directly from and over Windows 10, which worked well. Problem: W11 is now harassing me by displaying a permanent message to activate it. From what I've read the OEM is supposed to do that automatically, but it didn't and no key is to be found anywhere. I tried every chain of characters on the envelopes the DVD came in but it didn't work. I've tried the "troubleshoot" option in the Activation Settings menu. I assume it didn't work out because of my method of installation, so I tried the "I recently changed hardware on this device", which technically is true as basically everything except the HDD I installed W11 on is new, but that didn't work either. Windows is simply asking me to spend another 200 something € after I've already spend a lot of money on the OEM. And yes, I've bought the OEM from a reputable source (alternate.de) which has been in business for over 30 years and is a known and trusted retailer of hard and software. I buy everything there and never had issues. So yeah, I'm at wits end.