Declerations of war are not really a thing anymore in international law. Its not like usa ever declared war on Vietnam, but it clearly was one. Ditto for the iraq war. And its not just USA either. Declerations of war more or less stopped being a thing after the UN charter was signed.

You're right that that makes it messy. The us wasn't engaged in an armed conflict with the state of yemen, but with a non-state armed actor operating within yemen (and elsewhere). (And its not like that isn't true right now either - america bombed houthi positions in yemen just a few weeks ago. Different group but still a non-state armed group i would consider america to be in an armed conflict with). A lot of the ways we think about wars and what is just and unjust implicitly assume two states fighting each other. Its much more ambigious with non-state armed actors.