I got a similar but completely opposite issue.

I got 2 versions of FFXIV. A square store version i bought first and the steam version later when it was on sale for the steam overlay. Now when i went to buy Heavensward i thought it would be best to buy the steam version since i had zero issues with it so far.
However, now that i actually finished the story and the game said i didn't have HW installed some alarm was going on. I checked steam and it said it was installed so did some research and found out that you have to activate on mog station as well on your account. So i thought ok let's do this and tried 3 times but my steam HW key got refused. Big alarm in my head and did some more research and it seems that if you bought a mog station account first you cannot add the steam HW code on it. So i essentially bought 35euro of useless code.
I am not requesting a steam refund but you can be sure if i don't get it, i will straight up quit this game. The 2 versions are not compatible even tough on the site it saids they are identical.