To what extent do the different levels of the Executive Branch help to reinforce the democratic principle of Federalism?
The different levels of the national government's executive branch really do not help to reinforce the principle of federalism in any major way. Federalism is the idea that the states and the federal governments should share power. The different levels of the federal executive are all controlled by the federal government and not by the states.
I suppose that you could argue that federalism is reinforced when a federal agency has offices in various states. But that really doesn't do much for federalism. The federal agencies don't answer to the state governments. Instead, they generally tell them what to do.
So unless I am misunderstanding what you mean by "levels" of the executive, there is no real way in which they reinforce federalism.