You call out Article III, for example, so I'll focus on that. It doesn't say "we should have a Supreme Court and other courts Congress may establish." It says the judicial power of the United States shall be vested in them, and that judges shall be appointed. It isn't magisterial or clerical power. It clearly establishes the United States as a common law system. That's further reinforced by the use of the term jurisdiction — literally the power to say what the law is. It's clear that any and all courts established by Congress are "inferior" to the Supreme Court, which is a significant protection of judicial independence. It's also clear that Congress can't reduce their pay as retribution - ditto. And that's just the first section.
It's a much richer document than your previous comment gives it credit for.