How come you didn't need to set firewall permissions for the production instance? Does Azure Sql Server automatically allow any incoming connections from container instances?
A little late, but you can use managed identities and assign your container app a role in the SQL server in Azure. You assign the identity to the container. Then you use a special connection string that will tell your apo to authorize with Managed identity. You also need to add users and roles in each database for each accessing service. Azure can’t do that for you.