@Ho, Eddie Thank you for reaching out.
Sorry to hear about the issue you are facing while connecting to an Azure SQL DB from ADS via SSH tunnel gives you error.
It is not possible to connect via SSH tunnel - there is a request for that: Feature request: built-in SSH tunneling · Issue #398 · microsoft/azuredatastudio (github.com)
You can upvote it and add comments as it still exists in our backlog.
Regards,
Oury