Privacy options for important members of an organization

I work for the IT department at a university and we are soon shifting all staff members to be on Teams. The dean has a concern about their privacy though, as they don't want to be directly accessible to people, they only want a few of their employees to be able to chat them over Teams. My understanding is that the Do Not Disturb setting, with the allotment of permissions for certain people, would be a decent approach at solving this problem. My only concern, is that any time they have to log out/back in to Teams, their status would reset and they would get any messages that were blocked while they were on DND. Are there any backend solutions to this problem (or any simple frontend solutions that I'm missing)?