Hi,
Same problem here: I can see the game in my library, but if I try to install it, the EA app says: I don’t have this software. I have the box for this game, so I’ll try to add this using the serial number; it says "series already used" (oh really, yes because that’s the game I bought and added to my account from EA, formerly Origin, a few years ago!)
It would be interesting for EA to fulfill its end-user license contract by giving access to the game we bought from them, because the more years go by, the less it makes me want to invest in their licenses. I had a similar problem with the command and conquer tiberium war. It was impossible to reinstall it and play there several years later.
We pay a high price for games to have much worse follow-up than that of the small, independent studios.