Just to clarify, but if you log into the Mogstation, where it says your account type, does it say "Standard" or "Standard (Steam)"?

I'm not entirely sure your account will be the Steam version if you only did the free trial through Steam (I could be wrong, but people seem to have said different things and since I didn't do it this way myself...). Whatever the Mogstation says for account type is the thing to focus on though.

If it doesn't say Steam then you can just buy HW from anywhere you want (as long as it's the non-Steam version).