This example was used in the article to show how the kids are randomly sent stimulations for which they are not prepared. Plausible, but unproven (not that this article pretends to be science; it's a collection of useful anecdotes with some reflections on them).
Getting your marks sent to you when you are in a different context is private; you can feel shame or stress and in fact not know how you rank vs your peers.
The social stress isn't that new, and as far as marks went both my parents grew up under systems where the marks were posted outside the classroom and class ranking was also public.
I was really struck about the "prepared" part -- a lot of this should be considered spam: I don't need to know my marks (or bank balance etc) in realtime; I want to be able to get that info when I am ready to ask for it. The continual barrage of requests for attention is itself stressful. Having access to uninterrupted quiet (and boredom, especially for younger kids) is important for mental health and creativity.
Social has its own positive place as well. HN is a form of that.
I'm using the sociological sense where "private" means "to one's self" and "social" or "public" mean "part of a common experience or utterance with at least one other person" because I think that's the important distinction in this thread.
I'm not sure why anyone's surprised, either. Getting a reply to a critical work email is a little like getting a report-card grade, and it can arrive at any time of day.
Not that we need analogies (yet) in this discussion, but if someone dies in a plane crash, their autopsy report will probably say something like "blunt-force trauma to the brain" as cause of death. That is absolutely correct, but it's also absolutely true that the person would still be dead even if the Flying Spaghetti Monster had intervened and prevented the blunt-force trauma to the person's brain.
Delete Facebook/Instagram from the world, and kids will still be anxious.
By contrast, many adults would think of school-related apps as "like work", so ok.
You just say "assignments will be posted on App" and then the students are required to use it (or bum off of a friend).