Unfortunately, the chart "Background color" offers only a single choice.
Chart editor > Customize > Chart Style > Background color
You Could Simulate Background Colors
You could however simulate different background colors by strategically filling cells located behind the chart.
Simulated Background Colors
- Create a chart with a clear background;
- Hide (uncheck) "Gridlines"
"View" (menu) > "Show" > "Gridlines"
- Color the cells beside your chart ("Fill color");
- Drag your chart on top of the colored cells;
- Tweak column widths and row heights as necessary;
Hide (uncheck) "Gridlines"
Color the cells beside your chart
Drag your chart on top of the colored cells
Note: I repurposed the Line Chart from this solution