Flutter overlayEntry doesn't update content after state change

I’m trying to implement an overlay function for a text field that shows some particular state depending on what’s the user input. When the user taps the text field, it will display an overlay that should show some information while the user is writing, much like a search bar on a web browser works.

My problem is that the content of the OverlayEntry doesn’t update at the same time the user input change, it only changes when I reopen the Overlay.

Expected behavior

Current behaviour

For testing this functionality, I’m just passing the same value from the text field to the overlay.

This is my code:

Home class

class MyHomePage extends StatefulWidget {
  const MyHomePage({super.key, required this.title});

  final String title;

  @override
  State<MyHomePage> createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  @override
  Widget build(BuildContext context) {
    return GestureDetector(
        onTap: () => FocusManager.instance.primaryFocus?.unfocus(),
        child: Scaffold(
          appBar: AppBar(
            title: Text(widget.title),
          ),
          body: Center(
            child: Column(
                mainAxisAlignment: MainAxisAlignment.center,
                children: <Widget>[
                  CustomTextField(),
                ]),
            // This trailing comma makes auto-formatting nicer for build methods.
          ),
        ));
  }
}

Custom Text field class:

class CustomTextField extends StatefulWidget {
  CustomTextField({Key? key}) : super(key: key);

  @override
  State<CustomTextField> createState() => _CustomTextFieldState();
}

class _CustomTextFieldState extends State<CustomTextField>
    with TickerProviderStateMixin {
  TextEditingController controlador = TextEditingController();
  FocusNode nodeUno = FocusNode();
  OverlayEntry? _overlayEntry;
  GlobalKey globalKey = GlobalKey();
  final LayerLink _layerLink = LayerLink();
  String inputText = '';

  @override
  void initState() {
    super.initState();
    OverlayState? overlayState = Overlay.of(context);
    WidgetsBinding.instance!.addPostFrameCallback((_) {
      globalKey;
    });

    nodeUno.addListener(() {
      if (nodeUno.hasFocus) {
        _overlayEntry = _createOverlay(inputText);

        overlayState!.insert(_overlayEntry!);
      } else {
        _overlayEntry!.remove();
      }
    });
  }

  OverlayEntry _createOverlay([String? text]) {
    RenderBox renderBox = context.findRenderObject() as RenderBox;

    var size = renderBox.size;
    return OverlayEntry(
        builder: (context) => Positioned(
              width: size.width,
              child: CompositedTransformFollower(
                link: _layerLink,
                showWhenUnlinked: false,
                offset: Offset(0.0, size.height + 5.0),
                child: Material(
                  elevation: 5.0,
                  child: Column(
                    children: [
                      ListTile(
                        title: text != '' ? Text(text!) : const Text('data'),
                      ),
                    ],
                  ),
                ),
              ),
            ));
  }

  @override
  Widget build(BuildContext context) {
    return SizedBox(
      width: 250,
      child: CompositedTransformTarget(
        link: _layerLink,
        child: TextField(
          focusNode: nodeUno,
          controller: controlador,
          onChanged: (value) {
            print(value);
            setState(() {
              inputText = value;
            });
          },
        ),
      ),
    );
  }
}