I stand corrected. As you point out, the restrictions fall into the category of state restrictions and Federal restrictions. The Supreme Court has not ruled automatic weapons illegal, but it has upheld challenges to states banning them. Nor has it overturned those Federal restrictions you pointed out. So to the extent that the bump stock ban conforms to existing Federal law, it is not new law per se but enforcement of existing law.
There is no piece of existing federal law, to my knowledge, which prohibits devices which increase the rate of fire in legal SEMI-automatic firearms. That sort of catch-all language is part of the current gun control proposals, which just goes to prove that it's not yet on the books. Sessions is putting the cart before the horse with his announcement, probably with the expectations that some sort of gun control law will eventually be passed and close the circle.
As for why Sessions and Trump believe that political grandstanding on this topic is beneficial, it's a mystery to me. I think all it will do is lose Trump some supporters (not because of the gun issue specifically, but because they know mendacious political bullshit when they see it) and make the administration look amateurish and reactive.