Instead of SSMS use pgAdmin to connect to Azure Postgresql. You can download the software from here.
1.Open the pgAdmin application on your client computer.
2.From the toolbar go to Object, hover over Create, and select Server.
3.In the Create - Server dialog box, on the General tab, enter a unique friendly name for the server, such as mydemoserver.
I'm so late in posting. This is probably a group type permission issue. In order to get SQL Server group Windows Authentication for AD working, you will need to do the following steps:
Login as either Administrator or anyone (or yourself) who is a Domain Admin in the domain controller.
Open Active Directory Users and Computers and click Users.
Create a new ...