Faced a strange issue recently, was not able to publish a data entity to Bring Your Own Database (BYOD) while following Microsoft's manual. Right after I click Publish, the following two errors appeared in the Infolog: "Object reference not set to an instance of an object" and "Entity XYZ could not be published".
The solution was found here, it turns out that columstore indexes are supported from S3 Azure SQL tier level. If you want to use smaller/cheaper DB tier, you need to disable this option, or upgrade Azure SQL to S3 at least.