“How is this defined as an executive power?”
All the agencies that produce classified information are in the executive branch. All the agencies that decide what material should be classified are in the executive branch. All the agencies that determine who gets access to classified information are in the executive branch.
Classification is essentially an internal administrative designation for information produced by the executive branch.
Existence of said agencies does not verify their constitutionality, either way.
Even the Treasury Department’s constitutionality is not established. The power to “coin money, regulate the value thereof, and of foreign coin” is given to Congress by the Constitution, not the executive branch; “delegating” that power to the executive branch is a deliberate destruction of the separation of powers, even from the establishment of the USA.
PS. That is a circular argument that does not explain the constitutionality thereof, with all due respect.