How do I determine the public DNS resolver that's being used to resolve public internet addresses from laptop connected to a network? I can only see the internal DNS resolver address from running ipconfig in Windows.
You can try
dig whoami.akamai.net. The Akamai DNS servers are set to respond to this name with the IP address of the server that requested it, so that shows you the farthest upstream dns server in that chain.
Otherwise, no. Unless somebody decides to advertise it, there's no way to find out who their upstream DNS is.