As implied a Personal (or Parental) Overwatch Drone, was designed as a security measure to keep Hatchlings under control. It is about the size and shape of a football and is designed solely to keep kids out of danger. For example if a Hatchling were to try and walk into an off limits area, the POD would lock the door and prevent access through the door. If need be they can even physically block the doorway with a barrier. The barrier only blocks the delinquent, others can freely walk through it. If the child attempts to attack the POD, or someone else, it will immediately announce a warning to others and contain the delinquent inside a 'box' until they are deemed safe again.
The POD also monitors the behavior of the Hatchling. They have an AI that is designed to see if the child is upset, or happy. They are not capable of much in terms of emotionally boosting, conversation yes, but often this is where a real parent can step in and help directly. Which means yes it can act like a really smart baby monitor. The POD can directly connect the child and their parents together for direct communication.
In rare circumstances older dragons may be given these as a form of punishment, as it demeans their status, treating them like a baby instead of an adult.