Here is the Snippet to achieve toggling CupertinoSegmentedControl programmatically.
where sliderkey is given to CupertinoSegmentedControl widget.

 void toggle(int index) {
  final x = (sliderKey.currentContext!.findRenderObject() as RenderBox).size.width;
  (sliderKey.currentState as dynamic)?.onTapUp(TapUpDetails(
      kind: PointerDeviceKind.touch,
      localPosition: Offset(index * (x / (widget.children.length)), (widget.children.length + 1))));
}