Tbf the "deep state" bogeyman existed before Trump came to power. The deep state is all that policy, procedure and yes, bureaucracy, that support non-individualized spending of society's production on the working class, thus limiting growth of spending on the asset-renting class.
I agree, the deep state as not just a government bureaucracy but a structural force that limits wealth concentration. That’s not how most right-wing populists see it, but there’s an argument to be made that the real conflict isn’t between “the people” and the deep state, it’s between different elite factions, with the public caught in the middle.