I think there's room for a feature here: for approved contacts, notify them I'm busy when they try to call or message and ask if they want to interrupt. I think some desktop IM apps had that some time ago, but I haven't seen it on popular mobile equivalents.
The iPhone sorta has this with Focus Status Sharing and auto-reply to texts turned on. Clumsy/has caveats and is not quite what you said, but close enough to mention anyway.
iOS has this now with Focus Status Sharing; eg in messages others can see you’re busy and they caget extra options like ‘deliver quietly’ and ‘notify anyway’ - third party apps can do this too but not many have added it yet.
