The problem with the "spell attack" language is..... if it was that cut and dry why not just use that for innate sorcery?
When making a spell attack from a sorceror spell, you gain advantage.
That would remove any ambiguity. In the abscence of that, we have to take seriously that "attacks of a sorceror spell" might include non-spell attacks.
Bigby's hand was an example. Is it really that different that I create a construct that attacks for me using the magics of a spell, and my sword makes an attack using the magics of a spell?
Not that does open the door for summons and conjurations. If I summon a creature that attacks outside of my routine, do they get advantage on all of their attacks? (if you think the true strike = yes, than you likely would need to agree that the attacks of all summoned creatures also get advantage)