Read the W3C Recommendations for the protocol and data model. Neither has any mention whatsoever of a notification or alert:

https://www.w3.org/TR/annotation-protocol/

https://www.w3.org/TR/annotation-model/

Any type of notification would be an extra feature performed by annotation software, but is not a part of the specification.

Your annotation client could query the annotation server at a known endpoint for new annotations. The results should be ordered and paginated, but the order and pagination used seem to be at the discretion of individual implementations.