当前问题是_debounce尚未初始化。请将late改为可为空的Timer? _debounce;。
而变化将是

child: TextFormField(
  onChanged: (String text) async {
    if (_debounce != null && _debounce!.isActive) {
      _debounce!.cancel();
      _debounce = Timer(
        const Duration(milliseconds: 1000),
        () async {
          await searchText();
        },
      );
    }
  },

完整片段

import 'dart:async';
import 'dart:convert';

import 'package:http/http.dart' as http;
import 'package:flutter/material.dart';

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      debugShowCheckedModeBanner: false,
      home: HomePage(),
    );
  }
}

class HomePage extends StatefulWidget {
  @override
  State<HomePage> createState() => _HomePageState();
}

class _HomePageState extends State<HomePage> {
  String url = "https://owlbot.info/api/v4/dictionary/";
  String token = "7ba05536bd11ff8e22800cbda80951376c59ed84";
  TextEditingController textEditingController = TextEditingController();
  late StreamController _streamController;
  late Stream _stream;
  Timer? _debounce;

  Future<void> searchText() async {
    if (textEditingController.text.isEmpty) {
      _streamController.add(null);
      return;
    }
    _streamController.add("waiting");
    Uri uri = Uri.parse(url + textEditingController.text.trim());
    http.Response response =
        await http.get(uri, headers: {"Authorization": "Token " + token});
    _streamController.add(json.decode(response.body));
  }

  @override
  void initState() {
    super.initState();
    _streamController = StreamController();
    _stream = _streamController.stream;
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        backgroundColor: Colors.green,
        title: Text(
          "Dictionery",
          style: TextStyle(color: Colors.white),
        ),
        centerTitle: true,
        bottom: PreferredSize(
          preferredSize: Size.fromHeight(45),
          child: Row(
            children: [
              Expanded(
                child: Container(
                  margin: const EdgeInsets.only(left: 12, bottom: 11),
                  decoration: BoxDecoration(
                    color: Colors.white,
                    borderRadius: BorderRadius.circular(24),
                  ),
                  child: TextFormField(
                    onChanged: (String text) async {
                      if (_debounce != null && _debounce!.isActive) {
                        _debounce!.cancel();
                        _debounce = Timer(
                          const Duration(milliseconds: 1000),
                          () async {
                            await searchText();
                          },
                        );
                      }
                    },
                    controller: textEditingController,
                    decoration: InputDecoration(
                      hintText: "Search for Word",
                      contentPadding: const EdgeInsets.only(left: 24),
                      border: InputBorder.none,
                    ),
                  ),
                ),
              ),
              IconButton(
                icon: Icon(
                  Icons.search,
                  color: Colors.white,
                ),
                onPressed: () {
                  searchText();
                },
              ),
            ],
          ),
        ),
      ),
      body: Container(
        margin: EdgeInsets.all(8.0),
        child: StreamBuilder(
          builder: (BuildContext context, AsyncSnapshot snapshot) {
            if (snapshot.data == null) {
              return Center(
                child: Text('Enter A Search Word'),
              );
            }
            if (snapshot.data == "waiting") {
              return Center(
                child: CircularProgressIndicator(),
              );
            }

            return ListView.builder(
              itemCount: snapshot.data["defination"].length,
              itemBuilder: (BuildContext context, int index) {
                return ListBody(
                  children: [
                    Container(
                      color: Colors.grey[300],
                      child: ListTile(
                        leading: snapshot.data["definations"][index]
                                    ["image_url"] ==
                                null
                            ? null
                            : CircleAvatar(
                                backgroundImage: NetworkImage(snapshot
                                    .data["definations"][index]["image_url"]),
                              ),
                        title: Text(textEditingController.text.trim() +
                            "(" +
                            snapshot.data["definations"][index]["type"] +
                            ")"),
                      ),
                    ),
                    Padding(
                      padding: const EdgeInsets.all(8.0),
                      child: Text(
                          snapshot.data["defination"][index]["defination"]),
                    )
                  ],
                );
              },
            );
          },
          stream: _stream,
        ),
      ),
    );
  }
}