Where exactly did you buy your (i'm assuming HW) key from? If you bought from the SE online store there a notice on the page about steam.

Notice: This product is not compatible with the Steam version of FINAL FANTASY XIV: A Realm Reborn. If you’ve purchased FFXIV: A Realm Reborn on Steam, then you must also purchase FFXIV: Heavensward on Steam to upgrade your existing account.