From what I have gathered, if you wish to play FFXIV with Heavensward through Steam, you will have to get the Steam Heavensward version. Just because you're playing it through the Steam Client. You can also just simply download the installer from the FFXIV site and not play it through Steam. This should solve all your issues. Most likely this is also a consquence for being able to use Steam Wallet.

Your Squeenix account is seperate from Steam. There is no need for linking. If you check on Mogstation you will see it says 'Windows' copy. There is no seperate annotation for Steam.