Where to find a Win 10 product key after upgrade?

You can use NirSoft ProduKey to retrieve the product keys stored on your computer.

By definition, a traditional "clean install" will not have access to anything "on" your computer.

What happens is your key is stored in your MS account (at the MS servers) and that key is tied to your hardware hash for use with this machine only when your clean install "calls home" to activate... This is the old "Windows Product Activation" machinery moved to "The Cloud".

You needed an older key at first (long ago) for the "basis" of your upgrade and THAT was on your computer but this new system moves you forward to the "next step" or level...

Note: An "END USER" "Needing a key" with an OEM-SLP machine was not required "ever"... (Some exceptions or special cases exist.) That is another whole different family or license channel. This is also called BIOS locked...