Which seems like an enormous power grab on the one hand but I can’t really see any other way for them to be a check on the other branches without that power. There needs to be some legal basis to declare a law invalid. The Constitution (with all of its vagueness at times) seems like the better way than simply vibes.

The Supremacy Clause lists the supreme laws in order: constitution, federal statutes, treaties. If there is a conflict among them then it's natural for the courts to resolve that conflict by deferring to the more supreme item on that list, thus if a law violates -say- the right to due process as enshrined in the constitution then that law must be invalid and the courts must rule as much.

Marbury is an utterly natural consequence of the Supremacy Clause and Article III (and the context of common law).

This is all correct, of course, but misses the main point. There is nothing in the Constitution that proclaims the Supreme Court to be the arbiter of those conflicts. That's what Maybury did.

> Through their ruling of Marbury v. Madison, the court declared the Constitution as law.

The constitution declares itself as supreme law. See the Supremacy Clause:

  This Constitution, and the Laws of
  the United States which shall be
  made in Pursuance thereof; and all
  Treaties made, or which shall be
  made, under the Authority of the
  United States, shall be the supreme
  Law of the Land; and the Judges in
  every State shall be bound thereby,
  any thing in the Constitution or
  Laws of any State to the Contrary
  notwithstanding.

The order in which the supreme laws are given is: constitution, statutes, treaties.