The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.
No enforcement mechanism, no penalty for violation of oath.
That’s because Congress was to write those laws as to the enforcement mechanism, and the states the same with their jurisdictions. The Constitution was not meant to be explicit on those matters. Nevertheless, the Constitution explicitly calls oaths or affirmations binding.