And some of us over here, too.
That is a very fair question. Personally I think it is an error to consider this at all, but maybe not a totally obvious one.
Some of the protections in the Constitution are explicitly granted to “the people,” some to the States, and some are not so clear. Nowhere does the Bill of Rights mention citizens - only “people,” “persons,” etc. (The body of the Constitution does mention citizenship where it matters - eligibility for public office, for instance.) As to the rights of defendants in criminal trials specifically:
Amendment 4: search and seizure: protects “the people” and “the persons or things to be seized.”
Amendment 5: indictment by grand jury, double jeopardy, self-incrimination, due process: “no person” is subject to the prohibited acts.
Amendment 6: speedy and public trial, confrontation of witnesses, compulsory process for obtaining witnesses, assistance of counsel: “in all criminal prosecutions, the accused.”
Amendment 8: “Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.”
So at least the sixth and eighth amendments protect every accused, pretty clearly the 5th also, and very likely the fourth too. Personally I find it hard to understand how a criminal justice system could justify calling it “justice” to apply any of these rules on the basis of citizenship, legal residence, or any standard other than: this is justice, that other behavior isn’t. That is especially true when you consider that most of these rules - especially those in the 5th and 6th Amendments - are designed to protect not only the defendant but also the integrity of the system, specifically in regard to its ability to (reasonably) reliably result in truth.
No one knows but a handful of people in the Department of Justice. (And I do mean a handful.) If they are not subject to the jurisdiction of the courts, then there are only two legal statuses they could have, as far as I can tell: lawful prisoners of war, who must be subject to the laws of war, or unlawfully detained. In my opinion, the military has the legal right to hold people only as prisoners of war, or as strictly temporary detainees to be turned over to civilian authorities at the earliest opportunity.