The key is stored in the BIOS (UEFI flash chip) - you can install 10 or 11 from the downloaded installers MS offers; as long as the Home or Pro is correct it'll activate just fine.

You can verify the key exists by running

hexdump -C /sys/firmware/acpi/tables/MSDM

The salad is hanging out of the middle guy's pocket.

Reading package lists... Done

Building dependency tree... Done

E: Unable to locate package conset

If you have access to an external drive as big or bigger than the laptop drive, boot SystemRescueCD and ddrescue it as a backup, just to be safe. I personally haven't had it actually wipe a drive, basically it's saying switching might render it unbootable if the right drivers aren't in place.

I always back up first just to be safe though, worst case I waste a little time.