If the PS4 version you get via the insert in the PS5 case isn’t showing in your downloads list on a PS4 console, then I’m guessing that it’s a special PS4 build that can only be played on a PS5 console specifically for VR.
Though the insert doesn’t detail any sort of restriction like this on it, so I don’t see why you couldn’t download it onto a PS4 as long as you’re signed into the same PSN account.
Complete install your PS5 game and play HITMAN 3(online required)
Find VR mode access from main menu and open,then follow what webstore say.
ENSURE the code is redeemable under your playstation account region.