@KT Welcome to the Microsoft Q&A platform, thanks for posting the question and for using Azure Services.
We don't expose failed backup info as it is managed service, I don't think we expose this info that can be used for reporting. The following goes over how backups are taken
Backup and restore in Azure Database for PostgreSQL - Flexible Server | Microsoft Learn
There is no way to receive notifications about the backups. However, if you look at the backup and restore tab for the server, you will see the full backups available
Regards
Geetha