How does a Windows 10 'digital license' activate the OS?

Solution 1:

Does MS 'fingerprint' hardware information during the free upgrade / activation and store it, so that the next re-install queries MS for the fingerprint and activates Windows 10?

Yes; Windows has always been activated based off a hardware fingerprint though. Windows 10 has just made that process more transparent and with the most recent build made the process of transferring eligible retail licenses to another machine even easier.

A digital license (called a digital entitlement in Windows 10, Version 1511) is a method of activation in Windows 10 that doesn't require you to enter a product key. If you upgraded to Windows 10 for free from an activated copy of Windows 7 or Windows 8.1, you should have a digital license instead of a product key.

How does a Windows 10 'digital license' activate the OS?

The only difference between a traditional Windows license and a digital entitlement is that you no longer have to enter the license key when you install Windows 10 if you have a digital entitlement. Windows 10 will automatically activate. Additionally, and specifically optionally, is the ability to link your entitlement to your Microsoft Account.

Source: Activation in Windows 10

Thought the disk drive may change, I expect that none of the other fingerprinted hardware will change.

Windows activation status has never been connected to the HDD.