Games owned on Steam not appearing on EA despite linked accounts?

Hello. I have linked my EA and Steam accounts together. My understanding was that this allowed for playing EA games you owned on Steam through the EA app, but the game I have that fits this feature (Spore+it's DLC) is not appearing in my EA library. How do I fix this? Attached is a file showing both that I own the game on Steam, and that it isn't appearing in my EA library.