Currently we're seeing the republished state notification in different property where the republished library not exist. So its better to show the notification where it belongs to.
For example. Look at the below screenshot.
The republished library AppD belongs to different property but I can able to see the republished notification in above property where AppD Fixes library not exist at all.
Looks like its a Launch UI bug - but if it's not considered while implementation so sharing the post as an IDEA.