Yes, war is vested in Congress. However, the Executive Branch has wide latitude in taking action that is not considered “full war”.
Each President, nearly every one has filed objections to the Constitutionality of the War Powers Resolution. But, most simply veto the Bill.
Democrat Kane attempted the War Powers after Trump killed Iranian General Soleimani with a drone strike. Kane had no standing on War Powers so, drafted a separate resolution, which failed.
Do you have a Supreme Court decision or perhaps constitutional reference to the term “full war”? Or do you just make things up convince yourself putting your army in another country and killing their people is something less than war.