OK, I think I’ve figured it out. If you go to the game screen, select View Product, then select the …, then from that list select Final Fantasy VII Remake upgrade for PS4 owners, then on the next screen go to the version drop down and from there choose the second of two identical options named “Game”, then it does seems to add it to your PS library. I wish I was joking.
Edit: Pick the bottom “Game” or it won’t work, obviously.