If you don’t mind doing it yourself, you can always just draw it every frame before anything else. Even if it’s a single static image, I don’t think there’s a simpler way to do this. The background color is just what color “nothing” is, as in, when you haven’t drawn anything to the screen, what color it should be. You wouldn’t really even benefit from using layered destination textures if it’s just a single static image.
The tricky thing is taking into account multiple resolutions and aspect ratios, which I suppose is one tricky thing with 2D game development in general. You can scale either to height or width, though you might want to match the scale of the main game, and you need to consider that some people use aspect ratios anywhere from 4:3 up to 21:9, maybe more. What I’ve done in the past for backgrounds is double the game resolution on each axis, but it’s far from a perfect solution.