If he gave them an order, that's (by the SCOTUS) an official part of his job. Therefore, all information surrounding that action would be subject to immunity. So you couldn't even investigate that it was a misuse of his power.

As we've discussed, none of that is necessarily true.

If Biden gives an order that he is prohibited from giving under the Constitution, it's almost certainly not an official act. An official act is an exercise of the President's constitutional power. He's prohibited by the Constitution (not just criminal law) from assassinating someone. So this can't be an official act.

Second, while information regarding an official act is subject to immunity, that only means it's not admissible in a criminal trial to prove something about that official act. It doesn't mean it's not subject to investigation, and it doesn't mean it's not reviewable as part of a determination of whether his was (or was not) official.

Finally, WRT Gitmo - the President's official actions are immune from after the fact criminal prosecution, but they're still subject to the Court's ordinary jurisdiction. If the President does something unlawful, SCOTUS (or any federal court) can still order him to stop doing it. As the Court has done to Biden several times this term. He can't be criminally prosecuted having done something that violates a Congressional statute (for example), but the Court can order him to stop doing it.

So if Biden orders Trump to Gitmo without due process, the courts can (and would) order him to release Trump immediately, either through an injunction or a writ of habeus corpus - regardless of whether immunity attached to that act.