I have Sims 3 on Steam. I want to play Roaring Heights how do I download it?

I am in a similar predicament, owning sims 3 (all nearly all dlc) on steam instead of ea (although I do have the base game only on there from transferring the code some years ago). However, when buying the world, I had no choice but to buy it on the ea app, and I attempted to follow the method of redeeming a code on the sims 3 store site (which is linked to the same sims 3 account), but that did nothing. Is there anything else I could do to get it working, given I just spent £7.50 on roaring heights, and it would be annoying to see that money down the drain basically.