This is correct, although you wouldn't know it from the reeeeing from the usual suspects. Most people don't know any of the amendments in the Bill of Rights, except some vague notions from the 1st and 2nd, but the applicable amendment here is the Tenth Amendment:
The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.
Is the definition of marriage something expressly designated in the Constitution? No. Is it prohibited to the states in some way? No. Therefore the Supreme Court has no authority in this matter and has no right to declare that states may or may not outlaw interracial marriage.
It is the same as Obergefell v Hodges, the ruling that created a "right" for homosexuals to "marry" and of course the most infamous of all, Roe v Wade creating a "right" to murder unborn children. In all of these cases these are "rights" whipped up from thin air.
Senator Braun is 100% correct and pointing this out does not mean supporting bans on interracial marriage. That is a separate question. The question is: does the Supreme Court of the United States exist to create new laws because people have the sadz over a state law? Of course not.
Pointing out the obvious from a grade school understanding of the Constitution is now a "gotcha!" moment and Braun being mostly useless tried in vain to walk it back. He doesn't understand that you never, ever apologize to these people and especially not when you are right.
Further proof that the Constitution, whatever utility it once held, is now truly just a useless piece of paper.