The founding fathers did not see fit to include it, however they
could never have concieved of a power that could destroy our country, in the space of half an hour.Congress recognized that the President must have the authority to respond to any direct threat/attack. It could take days to get congress into session or in agreement, so the Congress gave the President the power to wage limited war in these emergencies.
In the current crisis congress gave the President almost unlimited powers. The President did not ask for a formal decleration of war, which I think was a mistake, and so did a few congressmen.
The Constitution you seem so intent on quoting to form your argument, gives the congress the authority to pass legislation, and in this case they did.
I think the reason or no formal decleration of war is purely political, in that the president and the military have practically unlimited powers, so congress holds them in check, by giving all the power, but with the safety valve installed.
PS. I am probably old enough to be your Papa
You can suck Truman's words, "I wish this never happened."