In Compatibility mode: canvas_item shader COLOR output is treated as sRGB (gamma-encoded). Video YUV→RGB math produces sRGB values → correct.
In Forward+ mode: canvas_item shader COLOR output is treated as linear color, then the engine automatically applies sRGB conversion for display. So the already-gamma-encoded video values get gamma-corrected a second time → everything becomes too bright/washed out. The viewport/hdr_2d=true in your project settings makes this worse.
The fix is: in Forward+ mode, linearize the RGB values before writing to COLOR (undoing the video's built-in gamma), so the engine's automatic conversion brings them back to the correct sRGB result on screen. I'll add a linearize_output uniform controlled by GDScript.
This fixed it for me. Maybe it will lead you to the core fix :)
