Update: There was a HP PN hidden on the back which was HP PN: 931738-001 which turned out to be from a HP Envy Desktop. With this information I was able to find the part itself online
(search:
https://www.google.com/search?q=hp+...rome..69i57.6863j0j7&sourceid=chrome&ie=UTF-8 )
(sale:
https://www.memory4less.com/hp-931738-001)
It does look like some people think it is a 480 though (Forum Post:
https://forums.overclockers.co.uk/threads/hp-oem-rx580-4gb.18828271/ ) This same post gave memory speed as well as processor speed, though I don't think it is correct for the PN in question.
At this point, I'll probably just try a few of the options in the "unverified" bios roms in the TechPowerUp VGA Bios Collection since I know the rough clock speed (1266MHz) from the Overclockers.uk post above. Looks like there are like 15 options that are for the 4GB variant of this card in that repository, though none for a 1266Mhz variant.
(I'll Try this one first, though it is for 1366 mhz
https://www.techpowerup.com/vgabios/210609/210609).
If anyone has the verified Bios File for the HP PN, though, I would still like to get my hands on the right one!