A control default button to be visible in the toolbar can be added using the activateUiButton method. This way, using the following react component would work and the draw rectangle mode would be available in the toolbar:
const modes = MapboxDraw.modes
modes['draw_rectangle'] = DrawRectangle;
// ...
<MapboxDraw>
modes={modes}
displayControlsDefault={false}
controls={{
polygon: true,
trash: true,
rectangle: true // custom control display
}}
</MapboxDraw>
A control default button to be visible in the toolbar can be added using the activateUiButton method. This way, using the following react component would work and the draw rectangle mode would be available in the toolbar: