The NY Times doesn’t use the words “dictatorship” or “autocracy” or “authoritarian,” because that’s not their way. But, with some good reporting, they show that Trump plans to make himself a dictator. He has calculated that he can reveal some of his plan in advance, to minimize the shock of the transition to complete autocracy.
He has calculated that no Republican will object. They will be his enablers.
I think if you listen to conservatives, conservatives make it clear that that's not what they're talking about.
In my experience, the extremely common meaning of "deep state" among conservatives is the civil service, the career employees of the federal government that they have disagreements with.
Of course, half the time the conservative using the word will be so uninformed about how the government functions that they won't know WHO they have an issue with, just that it's someone in there.