For migrating from Azure Database for PostgreSql to on-premise, I believe there is no service or tool handy at this moment but below is the article you can refer to.
Here we can create a .sql dump file from Azure Postgresql database and then you can import the dump .sql file in your on-premise database.
https://techcommunity.microsoft.com/t5/azure-database-for-postgresql/backup-azure-database-for-postgresql-to-a-blob-storage/ba-p/803343
You can also use the Azure Data Factory to achieve the desired functionality as well:
https://video2.skills-academy.com/en-us/azure/data-factory/connector-azure-database-for-postgresql
Hope this helps!
Let us know if you have any questions or need additional information.
Thank you!