@ZAS Welcome to the Microsoft Q&A platform and thanks for using Azure Services.
The Bestway you can do this is to remember the password and whenever you open Azure Data Studio, you can select the saved connection from the Connection drop-down menu in the Object Explorer pane to automatically connect to your server.
However, when the server is connected on running the new query it does not ask for a connection, for every query execution are you reconnecting?
Are you expecting to auto-connect to the server without selecting which server when you open Azure data studio? if yes then no unfortunately that is not possible.
Regards
Geetha