The obvious thing would be the 14th amendment due process clause. Can’t have a fair and unbiased case against someone if they’re the one judging it. Thats been affirmed as far back as The Federalist.
Beyond that, though I said it’d be up to the remaining 3 judges, I’m pretty sure it’d have to go up through the court system, and as Trump has shown, that can be slowboated to the end of time, or until those SC judges wisely decide to retire/get forcibly “retired”, after which the charges get dropped and everyone goes on their merry way, and then the courts (crazily enough!) establish again that the pres does not have that kind of immunity so history doesn’t repeat itself.
But I already know Joe wouldn’t play that kind of hardball.