rearmament happened in semi normal ways via giving contracts to companies, allow bidding. Do not check the production processes. This was all still done under the blanket of a normal economy (though the Nazis incurred massive debt that necessitated a war)

Total war footing of WW1 and WW2 implied the military administration / Nazi regime taking over all means of production to gear everything for the war effort e. By 1917/18 that meant intentionally stripping the agrarian sectors of manpower and resources to fuel the army for a last push (which meant requisiting last horses, drafting formerly essential workers and prioritizing the army for food supplies over food for the civilian population). Which in the end caused famine and shortages and a collapse at the home front.

The Nazis were very afraid of such a thing happening if it looked like they would repeat that until late into the war so they tried to maintain a facade of supplying basic goods normally.

So one can say they were already funneling lots of money into the military before WW2, more than the economy could afford, but various levers were left untouched until somewhere after Barbarossa failed.

Case in point for Barbarossa they still ordered tanks and planes normally and did not press for elevated production numbers, thinking it would be over like France anyway.

So sure, Germany had a more militarized economy than the western allies before WW2, but it did not activate all available levers necessary a totalitarian regime has available (see Soviet Union) until after their invasion of the Soviet Union failed.