Login failed for user when trying to connect to Azure Postgre database from MSSMS
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.



4.In the Create - Server dialog box, on the Connection tab, fill in the settings table.



5.Select Save.

6.In the Browser pane on the left, expand the Servers node. Select your server, for example, mydemoserver, to connect to it.

7.Expand the server node, and then expand Databases under it. The list should include your existing postgres database and any other databases you've created. You can create multiple databases per server with Azure Database for PostgreSQL.

8.Right-click Databases, select the Create menu, and then select Database.

9.Enter a database name of your choice in the Database field, such as mypgsqldb2.

10.Select the Owner for the database from the list box. Select your server admin login name, such as the example, my admin.



11.Select Save to create a new blank database.

12.In the Browser pane, you can see the database that you created in the list of databases under your server name.

For more details please read this documentation.