The timeout here is for the login, so if your credentials are the same on Dockers vs non-Docker, then your issue is likely related to connectivity.

From docker, are you able to reach the Azure SQL Database? By default, the Connection Policy is to use Proxy for connections external to Azure and Redirect to connections from Azure.

Redirect requires the port range 11000 to 11999 to be open, in addition to port 1433. Check if Docker can use this port.

There are quite a few assumptions here, but can only help more if you provide a bit more detail on the networking setup you're using. SQL Server settings, where Docker is connecting from, Firewall rules, etc.