I think your analysis of the role of finance capital in imperialism is correct.

State led doesn’t care about the profitability much, they want stuff done in accordance with the goals of the state.

This part i don't fully agree with. We cannot speak of "the state" in the abstract as the state is an instrument of class rule. And if we are talking about a bourgeois state then the "goals of the state" are the goals of the bourgeoisie, and more specifically the section of that class whose interests it represents. Which means that they do care about profitability, but whose profitability? To answer this question we again have to analyze the precise class character of the state in question...national bourgeois, comprador, finance imperialist, etc.

The problem is that the logic of capitalism eventually dictates that even if you do have a bourgeois state that for the time being serves first and foremost the interests of industrial capital, the natural progression of capitalism toward a falling rate of profit compels the system toward financialization and imperialism in order to maintain profitability. And that is if it actually manages to retain its independence and not become subjugated by a foreign imperialist power thereby turning comprador.