I believe the second SCOTUS case to which you are referring is HAMDI V. RUMSFELD.
https://www.law.cornell.edu/supct/html/03-6696.ZO.html
Thanks for refreshing my recollection that the SC did take up the issue after 9/11. The case I was referring to was Ex Parte Quirin, from 1942.
I reviewed Hamd. Hamdi found that an enemy combatant who contests being an enemy combatant may use habeas corpus in the US courts to determine if he is in fact an enemy combatant. It does not preclude the possibility that a military tribunal may be the decision maker, so long as a fair process is employed. Hamdi was a plurality ruling, so its use as precedent is questionable. Interesting, Scalia dissented because he thought the plurality went too far, and Thomas dissented because he didn’t think it went far enough.
With Kavanaugh on the court, the ruling might get to 5 if you add Kavanaugh, Gorsuch and Alito to Breyer and Roberts. If you don’t get all 5 of them, it would be another plurality, or worse. Breyer might change his mind, too.