Sc standard works fine when my computer is connected via wifi, but when I switch to a direct ethernet-to-router connection I can't hear the studio. Is there some setting in the router I need to open or change? Firewall?
It sounds like port forwarding has been set up for your WiFi connection. This means that your router is trying to send all incoming Source-Connect traffic over WiFi which is why your Ethernet connection isn't working. You will need to modify your port forwarding rules to forward the traffic to your computers Ethernet interface (it will have a different IP address from your computers WiFi interface).
If you have someone who manages your network you can ask them to do this for you. If you need help with this and you have an active support contract you can also book a support session at source-elements.com/book.
Port Forwarding is a setup in your router not your computer. source-connect defaults to UDP ports 6000 and 6001. There are free guides for most every router on the market and applications including Source-Connect at port forward.com