I am not with Laminar Research; just a flight simmer.
The following comments are based on your digital download being made directly with Laminar Research ie an original and official version of x-plane and not the 3rd party hybrid steam version which is not sold by Laminar Research.
Provided you have either installed X-plane "in total" onto your desktop or a dedicated drive and not mixed the installation with other directories/files on your hard disc then perform a complete copy of the files onto a reasonable capacity portable storage device and then paste onto your new storage location. No need to "fluff" around looking for your digital key.
You should have safely recorded the digital key on the basis you may need it again someday. What you are now seeking is that "someday"
Go back through your correspondence with Laminar Research when you purchased X-Plane. The "key"details were provided within that correspondence.
Failing all of the above contact Laminar Research at [email protected]
This email address has been created for those flight simmers who have "lost" their product key. However, you will need to provide details of proof of purchase etc.