Hello. I didn’t see a question directly asked, but I think I get you. The answer is obvious; Azure requires Azure AD authentication, cf. https://learn.microsoft.com/en-us/sql/relational-databases/security/authentication-access/azure-ad-authentication-sql-server-overview?view=sql-server-ver16
Make sure your version of SSMS is the latest and that you have Azure development configured as an installation option and you should see the Azure authentication options available. If you’re government, you’ll almost certainly be using MFA.
Please see below an example of what your dropdown should appear like when you have the proper components installed.