I would love for you to briefly describe how and where this can be done. I wasted a significant amount of time searching for this exact capability for Azure SQL Database and only ran into dead-ends.
For Azure SQL Database, you can restore any database backup to a new database, and export any existing database to bacpac format on a storage account [0]. The storage account file can be downloaded. You can also do the latter without using through the portal, using sqlpackage.exe on your local machine (same restriction applies: sqlpackage must connect to a live database, so if you want to download/view an Azure backup you must first perform a backup restore).
Not sure how to do the same for Azure Postgresql databases, but looks like standard pg_dump and pg_restore are supported.
I would love for you to briefly describe how and where this can be done. I wasted a significant amount of time searching for this exact capability for Azure SQL Database and only ran into dead-ends.