【Flutter】 日本語入力がONの状態でキーイベントを取得したい

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

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({super.key});
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        colorScheme: ColorScheme.fromSeed(seedColor: Colors.deepPurple),
        useMaterial3: true,
      ),
      home: const MyHomePage(title: 'Flutter Demo Home Page'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  const MyHomePage({super.key, required this.title});
  final String title;
  @override
  State<MyHomePage> createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  var _controller = TextEditingController();
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        backgroundColor: Theme.of(context).colorScheme.inversePrimary,
        title: Text(widget.title),
      ),
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            const Text(
              '@key を押すと hoge と入力される。',
            ),
            Focus(
              autofocus: true,
              onKeyEvent: (node, event) {
                if (event is KeyDownEvent) {
                  if (event.logicalKey == LogicalKeyboardKey.backquote) { // なぜか .at ではなく .backquote で検出。
                    const hoge = 'hoge';
                    final oldText = _controller.text;
                    final selection = _controller.selection;
                    final newText = oldText.replaceRange(selection.start, selection.end, hoge);
                    final newSelection = TextSelection.fromPosition(TextPosition(offset: selection.start + hoge.length));
                    _controller.value = _controller.value.copyWith(
                      text: newText,
                      selection: newSelection,
                    );
                    return KeyEventResult.handled;
                  }
                }
                return KeyEventResult.ignored;
              },
              child: TextField(
                controller: _controller,
              ),
            ),
          ],
        ),
      ),
    );
  }
}

if (event is KeyDownEvent) {
    _controller.text = event.logicalKey.toString();