Bumping this thread since I have the exact same problem and am getting very frustrated with the situation. The game in question (FIFA 16) shows up in my order history but not in the game library on the EA Deskopt App (PC). Contacting customer support did not help either, but rather directed to these forums.
I also reported my case in this thread (like dozens of other people) but so far I haven't received a response or any help:
https://forums.ea.com/discussions/ea-app-technical-issues-en/investigation-missing-gamesdlcs-in-ea-app-library-feb-2024---non-temporary/
Attention by community managers would be very much appreciated. Please help us recover access to our purchased games!