Is CREATE EXTERNAL DATA SOURCE Azure PaaS elastic databases broken?
You need to create the db scoped credential and the external data source all on the same (destination) database.

The IDENTITY='' should be an account that has access to the source database where you want to query from, in my example Test2.

So for example to access database Test2's tables from database test, execute all this on the database: Test.

USE TEST
CREATE MASTER KEY ENCRYPTION BY PASSWORD = 'STRONGP@SSWORD124321';
GO
CREATE DATABASE SCOPED CREDENTIAL CRED_Azure_Login
WITH IDENTITY = 'SomeUser', SECRET = 'STRONGP@SSWORD124321' -- this user needs to  have sufficient rights on the test2 db.
GO

CREATE EXTERNAL DATA SOURCE Source_AzureDatabase
WITH
(
    TYPE=RDBMS,
    LOCATION='&lt;DB location&gt;.database.windows.net',
    DATABASE_NAME='Test2',
    CREDENTIAL= CRED_Azure_Login
);

CREATE EXTERNAL TABLE [dbo].[test]
([Test ID] int)
WITH
(
DATA_SOURCE= Source_AzureDatabase
);


Source