Push and in-app notifications get read in isolation — on a lock screen, in a notification tray. "You have a new notification" carries zero information there, so users have to open the app just to find out, and eventually turn notifications off entirely.
A good notification packs sender, action, and object into one line: "Minsu commented: 'This looks great!'" The exception is sensitive content (health, finance), where hiding detail behind "You have an update" is the right call — the risk of lock-screen exposure outweighs the convenience.
The demo's ✕ tells you nothing even in the tray; ✓ is complete on its own.
When to use
Include sender and content for comments, likes, and messages. Make an exception for payment or health notifications and keep them vague.