"an object cannot be used as money unless, at the moment when its use as money begins, it already possesses an objective exchange-value based on some other use."
It’s right there. That’s what Mises said. If you’re going to concede (even for the sake of argument) that bitcoin is being used as a money then I don’t see how you can claim that it doesn’t violate what Mises just said.
Paper money has value because it is fiat…which means by decree. It is largely valuable because legal tender laws enforce its acceptance. (see this recent thread.) I think you’re misunderstanding the application of the theorem here. It is not so much “where does it get its value” as much as how the new money got priced in relation to other goods. His point was that without a prior exchange ratio there would be no way to know how much a unit would/should exchange for.
AKA “a money”.