I’ve seen dramaturgs listed in the artistic staff section with the director and designers. It’s usually if the show has a real historical relevance or was translated from another language or something.
Dramaturgs.
The phrase you’re looking for is “Resident Dramaturg.” Probably.
Production Stage Managers, sometimes called Production Managers, outrank Stage Managers, for one. They’re also sometimes a step removed from the artistic process; regular stage managers attend rehearsals and call cues during a show, while a production manager might oversee several stage managers working on several shows (especially in a large repertory company) and spend more time scheduling rehearsal spaces than actually being at rehearsal. In a theater which exists mostly as a space to be rented by traveling and touring companies, a PSM mostly hires crews and schedules the use of the space.
Confusingly, I’ve heard the phrase “Production Stage Manager” refer to the stage manager who calls shows for long-running productions, in contrast to rehearsal stage managers, who might only deal with the rehearsal process. It’s a vague and confusing job description, and the only thing that you can safely guess is that a PSM outranks an SM.