flutter webview doesn't work with dpad on android tv

Question

there is simple code snippet

import 'package:flutter/material.dart';
import 'package:flutter_inappwebview/flutter_inappwebview.dart';

void main() {
  runApp(
    MaterialApp(
      debugShowCheckedModeBanner: false,
      home: Scaffold(
        body: InAppWebView(
          initialUrlRequest: URLRequest(url: Uri.parse('https://github.com')),
        ),
      ),
    ),
  );
}

I created an android tv emulator and run this code.
It shows loaded google site but I can't change focus by pressing Tab button on my phisycal keyboard and dpad doesn't work either.
Also I tried on the real android tv device.

Anyone know how to fix it?
I think I'm missing something trivial here.

I'm using RawKeyboard.instance.addListener(_keyboardListener);

  void _keyboardListener(RawKeyEvent event) {
    if (event.runtimeType != RawKeyDownEvent) return;
    if (LogicalKeyboardKey.arrowLeft == event.logicalKey) {
      \\
    } else if (LogicalKeyboardKey.arrowRight == event.logicalKey) {
     \\
    } else if (LogicalKeyboardKey.arrowUp == event.logicalKey) {
      index = index - 1;
    } else if (LogicalKeyboardKey.arrowDown == event.logicalKey) {
      index = index + 1;
    index = index.clamp(0, maxIndex);
    _controller?.evaluateJavascript(
      source: ''
          'var arr = document.querySelectorAll("[tabindex]:not([tabindex=\\"-1\\"])");'
          'arr[$index].focus();'
          'var ss = arr[$index];'
          'console.log("---!!--" + $index);',
    );
  }

Where int index = 0; is index of focused html element.
On emulator I have to click somewhere on web page background and after that I'm able to move focus down and up.

The main issue is I can't do it on real device :)

UPDATE: ok, there is new info
before I tested it with some url then I can't show here. But for example I specified goodle url. And it works. Even I don't need to add listeners and run scripts.

But then I tried with https://github.com and it won't work.