with SDK for ArcGIS Pro 2.1 notifications are available for ArcGIS Pro.
I found this in the ArcGIS Pro help ArcGIS Pro notifications—ArcGIS Pro | ArcGIS Desktop
At the ProSnippets Framework · Esri/arcgis-pro-sdk Wiki · GitHub I found how to
Add a toast notification
Is it possible to create a blue dot if notifications are available instead of the toast notification?