But isn’t the Trinity really just three different manifestations of the same being, similar to how Pallas and Nike were both really Athena?
Yes, something like that. But I’ve spoken with Muslims who just think “You Christians believe in three gods”. My limited experience with their theology is that it is pretty limited — they do not want to believe in anything that is not completely obvious on the face of it, so “different manifestations of the same being” wouldn’t even make any sense to them.