Ah I don’t know much about sunshine and your specific setup. But I know docker can be a pain getting access to devices like graphics cards. Maybe try running natively?
I guess what problems are you having? I’ve used steam link before perfectly fine but it’s going to have some loss over the network. Are both computers connected to a gigabit lan? Balder’s gate 3 is a newer game, and while you aren’t on minimum requirements you are on mid tier hardware using proton to run a windows game, so there are a few reasons you may be having problems. Best way to run it down is isolate things and see how they go. Try running game directly on the computer with monitor ect.
Recently got a switch. Digital games are same price as physical, locked to my account/switch and saves don’t move easily between devices. Steam deck, I can play on any hardware that can support it TV, PC laptop games cloud save for free. I can play online games for free. I know that games I buy today will be available in 10 years on my next PC. I only buy carts for the switch cause they give me more flexibility still not even the same as steam.