And for future readers: If you have ever had a fully activated Windows 10 installation on a machine, and have not changed out the motherboard (and even on occasion when you have, but you have to call MS afterward), Windows 10 in the edition that was activated is still tied to that machine by a digital license.
If the activation doesn't occur on its own within a few days, then call Microsoft. They'll generally have you reactivated in under 10 minutes. I call Microsoft immediately if the activation does not take place automatically as part of the Windows 10 reinstall.
It's not necessary to buy an additional license.