The $Color of an item in Map is used to draw the title ($Name) of an item in Outline. So, if i understand it correctly you’d want a note with a ‘red’ $Color on the map to show in Outline as a lighter red? Here are a couple of stamps to try:
$OutlineBackgroundColor.saturation = $Color.saturation*0.5;
For more on colour manipulation see the dot-operators for the Color data type here.