Hello matrixino.

I'd suggest using something like the "Steam Web Integration" script that clearly informs you about every title you already own or don't own yet - not only on Steamgifts but on any page as long as there's a Steam link to the game. This helps avoiding joining for titles one already owns when you don't want to check your library manually for every giveaway.
You still being able to join although your SG is synched and using ESGST shows the shortcoming with the Steam API - which doesn't properly work when it comes to what DLC you already own.