Every day, millions of federal workers go to work, doing their jobs to the best of their abilities in accordance with the laws of the United States, and the regulations and policies that govern their particular tasks. That, I'm afraid, is what the "deep state" now is, according to Donald Trump and his cohorts: government workers, doing their jobs, following the rules; Lawyers following the law in the administration of justice; scientists gathering data and reporting the results; economists trying to suss out economic trends and counteract negative effects; educators teaching.
When Dwight Eisenhower left office, he coined the phrase "Military-Industrial Complex" to describe what he saw as an unhealthy alliance between the arms industry and expansionist elements within the military acquisition leadership. This morphed over time into the far more amorphous "deep state" of paranoid minds and fiction writers (think, Manchurian Candidate). In the conspiratorial mind, any action which doesn't follow their precept of what "should" happen becomes evidence of the conspiracy, no, matter the mundane and easily identified root of the "deviation". Because Donald Trump has deviated so far from the norms and traditions (not to say rules and laws as well), there are innumerable activities that don't conform to his (fantasy) expectations.
Thence we get to our current condition, fostered by the unfortunate accession of the party (and Congress), that normal people, doing normal things, for routine reasons become part of the grand "deep state" conspiracy.