Hi, @DAVID SANCHEZ RODRIGUEZ
Welcome to Microsoft Q&A thanks for posting your question.
Great to hear that your issue is resolved! and thank you for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer.
Issue: Having trouble connecting to an Azure SQL database from SQL Management Studio using SQL authentication. you have already successfully connected using MFA authentication and SQL authentication with Power BI. you suspect that the issue may be related to the new "Microsoft Entra ID."
Solution: As you mentioned Yes, when connecting to an Azure SQL database using SQL authentication, you need to specify the name of the database you want to connect to. By default, SQL Management Studio will try to connect to the "master" database. To connect to a specific database, you can either specify the database name in the connection string or select the database from the drop-down list in SQL Management Studio after connecting to the SQL Server instance.
If you have any other questions or are still running into more issues, please let us know.
Regards Geetha