“Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.”
Article IV section 1.
I’m still not seeing marriage definition there. From a practical standpoint, if the FedGov were the sole authority in defining marriage, then it would also have to be the sole authority to define divorce. It does not, the states do; that’s because its a state issue. Visas and passports are issued by the federal government; marriage certificates are issued by the state.