Add Shadow of the Tomb Raider to Library (PS4)?

This month there's "Shadow of the Tomb Raider" for free at Playstation Plus. I can add the other two free games to my library without any problems. But I can only download Tomb Raider. I've downloaded it now, but it's still not in my library.

Why is that? Do you have a tip for this? And how is it with you?

I guess you can only have a certain amount of games in the library

That doesn't make any sense either. What if I bought a game now? Then your assumption would be that it would no longer be available to me if I should delete it from the console

Nene can download it at any time, doesn't have to lie around in the library.