Ahl Kitaab/mushrik
Also once itmam e hujjat was done shouldn’t they have been called mushrikeen because they took it as a creed of their religion even after it was clear?
Yes! Isn’t itmam e hujjat to conclusively deliver the truth to the addressees? They were doing shirk and the hujjat on them was to make it clear and transparent their shirk. If not this, what else was the hujjat about? And if the hujjat was about this, then why not treat them the same way as Mushriks?
Allah knows best and he didn’t call them Mushrikeen