Mac Studio connected to Starlink, has no Internet connection, but has all green lights saying connected

What DNS settings does it show?

Change DNS settings on Mac - Apple Support

Is the interface you want dragged to the top of the list?

Change the order of the network services your Mac uses - Apple Support

Have you checked the configuration of your router, to see if it has anything like a "allowed MAC addresses" list or "prohibited MAC addresses" list that is locking out your Mac Studio? That your router is set up to provide DHCP (auto-configuration) service to both addresses?

I'm thinking that you could have Layer 2 Ethernet or WiFi connectivity between your Mac Studio and your router, without necessarily having Layer 3 (TCP/IP) and firewall settings configured in the right way to let you get out to the Internet.

Note that your Mac Studio's Ethernet interface and WiFi interface each have their own hardware (MAC) address. You can view those in the Hardware tab in the Advanced… section of Network Preferences (for each interface).

what status is showing at

system preferences > Network ??

Does the port on the receiver have exactly ONE Ethernet adapter?

are you using the StarLink supplied adapter?

when you plug in an Ethernet cable does the satellite receiver still have POWER?

The default setup I have seen provides ONE port out of the receiver to the Router (which has no Ethernet ports either), and no Ethernet at all.

How does yours connect for Ethernet?