Case in 1957 essentially was in the same posture -- parties in a case were ticked at the judge for forcing them to a magistrate without their consent. They filed a writ of mandamus with the court of appeals, which granted it. The judge then filed his own appeal of the writ with SCOTUS, which heard the case on the merits rather than dismissing for lack of standing.
https://supreme.justia.com/cases/federal/us/352/249/
I’ll take your word for it. Will we be paying the freight on both sides?