I have no idea.I believe the windows side should be possible depending on the details but are you sure the Shield can do whatever you want it to with the two streams? Android is generally not known for it's multitasking capabilities.
Basically I want to stream the video from an scrcpy window, plus the default system audio
Thanks - yes I have just discovered that route (OBS Studio), and have been exploring it. It seems to do what I need, albeit with a more complex setup than I was hoping to get away with!It sounds like the typical live streaming setup, where you're using the audio from an external microphone so it might be worth looking in that area.
OBS or something like that may do what you want, although I don't have personal experience so I can't say for sure.