How to debug 'Login failed for user' on an Azure SQL database?

The error looks like you are able to connect to the server but the server rejects the login. Debugging in the server logs would help, so you are looking at the right place.

You can enable Azure SQL Database Auditing & Treat Detection. You can enable it on SQL Server instance level by opening your SQL Server resource and selecting Security / Auditing & Treat Detection. Select a storage account to store logs in Storage details (see picture below). For more information, see https://docs.microsoft.com/en-us/azure/sql-database/sql-database-auditing.

After enabling auditing try to login to your database. After that you can find the logs in the specified Azure Storage Account in blob container named sqldbauditlogs. The logs are in folder /servername/databasename/SqlDbAuditing_ServerAudit_NoRetention/yyyy-mm-dd/ in files with xel extension. You can download and open the .xel -file in SSMS (File / Open / File…). The xel file contains events and you can see login attempts there.

Event field succeeded tells if the login failed or not, and field server_principal_name contains the username in both cases. From text in field additional_information you can find error_code (in the xml). Error code 40615 is blocked by firewall and code 18456 is wrong username or password. (error codes from https://docs.microsoft.com/en-us/azure/sql-database/sql-database-develop-error-messages)

You can also find some information in the database system tables for analysing the connections, e.g. sys.event_log (see: https://docs.microsoft.com/en-us/sql/relational-databases/system-catalog-views/sys-event-log-azure-sql-database?view=azuresqldb-current).

More information on troubleshooting the Azure SQL Database connectivity can be found here: https://docs.microsoft.com/en-us/azure/sql-database/sql-database-troubleshoot-common-connection-issues.

I hope this helps you forward with debugging the connection.