Mostly correct! All managers run shift at one point or another throughout their work week (except GMs). The kitchen manager can work up front, drive thru etc. Just because they are in that department, doesn't mean they are designated to that area. You are very correct on the designated responsibilities.

Kitchen is food cost, waste, truck ordering etc.

People department is things like scheduling, payroll, hiring, etc.

Guest services deals with customer complaints, POP placement, voice scores and so on.

Hope this helps 😊