Thought the upgrade was tied to your hardware (motherboard/CPU) and a clean install after would be activated?
Absolutely 100% correct.
As long as the previous install had been effectively "Activated" on that machine and you are performing the same version and bit architecture install as was previously present on the old spinner.
You should be able to simply skip / do this later.... all prompts during the install for a product key and when it is up and running and you're signed on with your previous MS Account (not really necessary) you should be good to go.
As a matter of fact you should absolutely avoid any attempts at entering anything you think is a product key for Windows 10 because no such thing actually exists unless you have made a retail or OEM purchase.
There was some time when the activation service servers were overwhelmed an the activation took a while.
And often any attempts you made through the activation wizard to change key or enter new key will just complicate the issue.
Basically
Upgrade
Confirm that the upgrade is activated
Clean Install
No keys..... don't enter anything, just use the links that say skip or do this later every time.