You are right. Washington was truly the “First in war, first in peace and first in the hearts of his countrymen”, but don’t underestimate what Jackson did either.
He was a terrific general, defeating the Creeks at Horseshoe Bend in a brilliant action. He also captured Pensacola, hanged the British heads of the territory and took Florida from Spain. He also was Florida’s first governor.
I have read that his defeat of the British at New Orleans was the worst defeat the British Army ever suffered and the troops there were supposed to be among their best.
Actually the war of 1812 was a sideshow to the British.
The Peninsular War against France took priority.