Hi John •,
Welcome to Microsoft Q&A forum.
As I understand, you could not connect to Azure SQL Database from VS Code.
As per the error message, please check server name like server\instancename.
Make sure the server machine is reachable, example DNS can be resolve correctly, you are able to ping the server.
Refer similar error post here for solution options:
Could you please provide below information:
What is Network/Firewall setting for the existing server in place?
Please share sample code which you are using to establish connection.
Let us know your finding.
Thanks