Well, technically, Houthis' action is illegal but then so are the actions of Israel, especially about the Settlements, and technically so was the Russian invasion of Ukraine and so was the American invasion of Iraq in 2003. Even China lost to the International Court's ruling about the South China Sea conflict.
It is past time discussing the 'history' of global conflicts and about the 'legality' of actions taken before or now or even about the morality and the ethics of the ongoing conflicts. That's why I don't indulge in debating those issues much here or in the old PDF. Violence is the only way forward and violence will settle the winners and the losers, like it did in the two World Wars and many other minor wars since then or before. Very unfortunate and sad observation to make. But the world is inevitably hurtling toward a World War--it is truly the Law of the Jungle out there where the UNSC can pass any Resolution with no teeth to enforce that.
The Iran vs America dance is going on since 1979 with no direct war. I don't think the Americans want a direct war. No one does except the Israelis if they can totally bring Americans onboard for that.
We should all dread a regional war. All of us. Our lives will be different and probably more stressful and miserable. Only the war profiteers would be happy in case of a regional war which could very easily lead to to the World War III. Humanity is capable of repeating its fatal mistakes and right now there are no guardrails except the fear of M.A.D.