i have the problem i like to stream with playstation 1 to 5, but adding the tv as 2nd monitor to get overlays is very complicated.
so maybe add at "(main) screen share" an option for "connected screen" so you can stream wathever is on it: playstation 1-5, x-box or wathever can be connected to the screen.
you just need this option equiped and a cable (USB or HDMI) that connects with the screen. than you can switch the tv inputs without interupting the stream, needing HDMI-splitters or extra applications.
you just stream the screen as the screen.