The Supreme Court blocks an order that would have inhibited third-country deportations, but it's not clear why; Kilmar Abrego Garcia gets a favorable (and long) ruling from a magistrate judge.
I think the difference between the third country case and the AEA case is 1252(f)(1) law not allowing case-wide relief from the immigration removal process, which does not apply to AEA.
I think the difference between the third country case and the AEA case is 1252(f)(1) law not allowing case-wide relief from the immigration removal process, which does not apply to AEA.