Sims 4 base game is free on Steam. If you install the base game through Steam it will unlock and download everything you own on EA and Steam. (Depending on how many packs you have it can take a while and I don't recall anything on steam telling me how long it would take... Steam just sort of seems to "discover' what you own and download it...)
However, it doesn't seem to work the same way if you own something on Steam and have everything installed through the EA app. Doesn't appear to be any communication from Steam to EA, just EA to Steam.