How To Recover A Nuked Stream Laptop

Working on a friends laptop for him. He gave it to me, after GeekSquad wouldn't fix it out of warranty. He said the power died during an update, and nuked it. Sure enough, it does boot to the black screen of death, saying it found no OS.

I started doing researching, running the SSN and model number. The recovery disk for the HP kit is $75 (and no alt option can be found online). It's a HP Stream 11-ak1012dx. I called tech support, and they don't cover the recovery disc. However, he did say something I found interesting that might fix it and save money.

It's a budget laptop that runs on eMMC using Windows 10 Home in S mode. I would have just installed a fresh copy of Windows from a thumb drive (like I've done millions of times), but I was afraid there would be an activation issue. My friend has no original discs or documentation. But the tech guy said the OEM key is stored internal. So simply reinstalling Windows will auto-activate.

I have two questions. This seems suspect, as I've never been able to auto-activate a new install of Windows without a key. Also, I don't have an S mode disc, just the full versions. Am I going to run into issues installing that without a proper key. I don't have anyone I know locally who can make me a S mode recover drive.