Why isn't this a "power" as well?

Because it's just a description of his oath. He has to, to the best of his ability, preserve protect and defend the Constitution. That doesn't mean that if he decides protecting the Constitution requires exercising Legislative authority that he can start enacting his own laws....or that defending the Constitution requires him to become judge, jury and executioner that he can start exercising Judicial powers. It's just the oath. He can't just say, "Well, I've decided that we need a mutual defense treaty to defend the Constitution, so I get to enter into that treaty without Senate consent."

There are no generic grants of unlimited authority to the President that give him the right to do whatever he wants just because he thinks it's a good idea - which is why every President ends up having some of their actions struck down by the Courts as being contrary to either the Constitution or statute. There's no broad power to do "anything necessary to accomplish goal X," whether goal X is the security of the country or protecting the Constitution.