Alien Enemies Act 1798, in part reads:-
“Whenever there Is a declared war between the United States and any foreign nation or government, or any invasion or predatory Incursion is perpetrated, attempted or threatened against the territory of the United States by any foreign nation or government, and the President makes public proclamation of the event, all natives, citizens, denizens, or
subjects of the hostile nation or government, being of the age of fourteen years and upward, who shall be within the United States and not actually naturalised, shall be liable to be apprehended, restrained, secured, and removed as alien enemies.”
So, invocation of the Alien Enemies Act 1798 requires either a declaration of war OR invasion etc type hostilities by a foreign powers AND a public declaration of such by the President.
If the cartels are tied to hostile foreign powers and there are actual hostilities taking place between the US and the relevant foreign powers, the Act can be legally invoked. POTUS has already made the necessary public announcements.
The hostilities we are currently witnessing by the US against various enemies may be a necessary prerequisite to invoke the Alien Enemies Act 1798.