Just to be clear on the terminology, a Color Scheme is for setting the colors used in syntax highlighting and in the editing area in general, while the color of the rest of the UI is done via a Theme. As such you can’t modify the background color of the Sidebar via editing a color scheme file.
I don’t have a lot of first hand experience with the modification of a themes but I think you need to modify the layer0 properties for the sidebar_container at a minimum. Some simple fiddling here on my end managed to make the entire thing jet black, so you probably want to also modify the labels to make the text more visible, for example.
As @remi pointed out, the Material Theme modifies the background color of the sidebar as soon as you activate it (as does the Boxy theme) so either one should set you on the correct path.
Also worth noting that in the latest round of Development builds (3127+, the latest of which at the moment being 3131) there is a built-in theme called Adaptive that does this automatically. You need to have a Sublime License to use the dev builds though (and theoretically it may be unstable in some fashion, but I’ve been using it for production work since it dropped with 0 problems, for what that’s worth).