"You don't need the product key" - while I appreciate the effort, I wouldn't have asked the question if this were true.
For others who come across this question and either have Linux natively installed or have access to a live install version, the key is located within the file at /sys/firmware/acpi/tables/MSDM and can be read with your favorite hex editor (like xxd); I'm sure there are equivilant MS tool(s) that can be used.
A quick note regarding my particular situation: I failed to log into my MS account when initially setting up my machine, because of that, when I went to use the product key, I received an error indicating that the hardware didn't match and the 'troubleshooting' steps I hoped to use to resolve my issue also failed because the product key was not associated with my MS account. In theory, if I'd done that initially, I would've been able to apply the key to changed hardware instead of needing to involve the help of MS Support.
An interesting explaination regarding MS product key management over the past few versions can be found here, for those looking for a better understanding of how this is managed by the MS operating system: https://arstechnica.com/civis/viewtopic.php?p=26623117&sid=1764d956bf32c105e4df0172a76e0442#p26623117