An Azure managed PostgreSQL database service for app development and deployment.
As mentioned by accepted answered by @GeethaThatipatri-MSFT , the best practice is indeed to create database per application/user instead of using default "postgres" database.
As per the design of PaaS environment, you cannot take dump of Postgres database as it is system database. We recommend you create separate user databases to store the data.
But if you are in that position, you can still perform your backup by appending the following flag to your pg_dump command: -N cron
Full example:
PGPASSWORD='your-pass' pg_dump postgres -h database-name.postgres.database.azure.com -U you-user -p 5432 -Z0 -Fc -N cron > postgres_dump.sql