要修复此问题，可以使用TabController的animateTo方法，通过动画更改索引

验证码：

class ScreenController extends GetxController with GetTickerProviderStateMixin {
  TabController? profileTabController;
  int profileInitialIndex = 0;
  int profileCurrentIndex = 0;

  @override
  void onInit() {
    profileTabController = TabController(
      vsync: this,
      length: 3,
      initialIndex: profileInitialIndex,
    );
    super.onInit();
  }

  void changeProfileTabbar(int index) async {
    print("Change Profile Tab 1: $index");

    // animate to the new index instead of setting it directly
    profileTabController!.animateTo(
      index >= 0 && index < 3 ? index : 0,
      duration: Duration(milliseconds: 300),
      curve: Curves.easeInOut,
    );

    print("Change Profile Tab 2: ${profileTabController!.index}");
    profileCurrentIndex = index >= 0 && index < 3 ? index : 0;
    print("Change Profile Tab 3: $profileCurrentIndex");
  }
}