The whole "oh yes, our military is active, but we aren't at war, and yes, the president tweeted about that" spiel is just untenable and ridiculous.
That is why this administration is leaning heavily into calling the drug traffickers "narco-terrorists" and calling fentanyl their "weapon of mass destruction". They're covering their ass legally so they can invade another country without congressional approval.
This is what they're using, the legal theory is basically tren de aragua cartel and their drugs is an "invasion" of the USA and is "sufficiently connected" to the Venezuelan government to trigger the act's wartime powers.