My question basically boils down to "does the Cabinet hold powers separate from the President?"

I'll give an example of what I mean.

The Secretary of Treasury is responsible for "[formulating and recommending domestic and international financial, economic, and tax policy, participating in the formulation of broad fiscal policies that have general significance for the economy, and managing the public debt](https://en.wikipedia.org/wiki/United_States_Secretary_of_the_Treasury)". Does the Sec. of Treasury have the powers described exclusively or can the President take on those responsibilities without a Secretary?

I know the President can remove a Cabinet member unilaterally and nominate a different Secretary if the former doesn't comply with their demands and a President won't likely nominate a Secretary that will disagree with them and refuse their demands. Still, if Congress writes and enacts a law that says "the Secretary of [Department] shall have the power to do such and such", is Congress giving that power directly to that Department/Secretary or is it granting that power to the President then allowing/directing him to delegate the powers to that Department?