I thought the Windows license was burned into the BIOS, so a reinstall would pick it up automatically?
Wrong. IT IS 100% stored in the UEFI firmware, specifically ACPI tables, MSDM field. Only if that exists, it is then verified on-line for activation to make sure the license is genuine and matches the device ID you're referring to for witch the license was sold(typically for OEM) or if it's portable.[1]
On linux you should be retrieve the license via something like:
sudo strings /sys/firmware/acpi/tables/MSDM
OR sudo acpidump | grep MSDM
[1] https://www.cyberciti.biz/faq/linux-find-windows-10-oem-prod...https://support.microsoft.com/en-us/windows/activate-windows...
https://superuser.com/questions/1575650/how-does-a-windows-d...
Btw ACPI is a specification, not a separate piece of hardware. ACPI tables are stored in BIOS nvram, there is no other place for it to go.