The error coming back from your SQLServer is that the read took too long and timed out, and before that error is emitted there are additional bytes written by the driver itself that it's also timing out while attempting what it calls a "prelogin":
Prelogin error: host ltgsql.database.windows.net port 1433 Error reading prelogin response: Read timed out
My best guess is that your Logstash node doesn't have a route to the target host. Maybe a firewall or VPN issue?