An Act Recognizing the existence of war..."
You are mistaken in your effort to impose a different standard on "declarations of war" than the historic record supports.
The truth is, you know very well the Confederacy issued a declaration of war, you just don't wish to call it that -- in the same way that Confederates wished to call slavery a "domestic institution".
You wish to nit-pick the wording, to assert that the Confederate declaration was not really a declaration, it was just a... well... a "recognition".
But regardless of whether you call it a "declaration" or "acknowledgement" or "recognition", the result is the same: Confederate President Jefferson Davis was granted war-powers and the entire Confederacy was put on a war-making basis.
Plus the Confederate Army was increased from 100,000 to 500,000 troops.
This at a time when the US army was still barely 15,000 troops.
So the historical reality on this subject is:
Bottom line: the Confederacy began making war six months before the Union did anything serious in response.
So you do admit that there was never any declaration of war by the Confederacy.