How to know exactly the moment the Back button is pressed to dismiss the Soft keyboard in flutter

I don't want to wait until the Soft keyboard has been dismissed.

The moment the user presses the back button to dismiss the keyboard I want to also at the same speed and time dismiss something else as well.

I attempted the following code to know when the user has pressed the back button to dismiss the soft keyboard

  @override
  Widget build(BuildContext context) {
    return WillPopScope(
      onWillPop: () async {
        print(
            "Back button has been pressed"); //This seems not to be called when the soft keyboard is been dismissed
        return true;
      },
      child: TextButton("Sample Button")),
    );
  }

I was surprised that the WillPopScope widgets' onWillPop method wasn't called when the softkeyboard was dismissed.

I don't want to use Keyboard Visibility package because that will only fire when the keyboard has been dismissed. Instead I want to know immediately the back button was pressed to dismiss the keyboard at that point in time.

class MyWidget extends StatefulWidget {
  @override
  _MyWidgetState createState() => _MyWidgetState();
}

class _MyWidgetState extends State<MyWidget> {
  final _focusNode = FocusNode();

  @override
  void initState() {
    super.initState();
    _focusNode.addListener(_onFocusChange);
  }

  @override
  void dispose() {
    _focusNode.removeListener(_onFocusChange);
    super.dispose();
  }

  void _onFocusChange() {
    if (!_focusNode.hasFocus) {
      print('Back button was pressed to dismiss keyboard');
      // Perform action you want here
    }
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: SafeArea(
        child: Center(
          child: ElevatedButton(
            onPressed: () {},
            child: Text('Sample Button'),
            autofocus: true,
            focusNode: _focusNode,
          ),
        ),
      ),
    );
  }
}