I am following a course to create a messaging application using flutter, and I followed all the steps to get the messages to Cloud Firestore, but in the end I do not receive anything.
this is the code:-

import 'package:cloud_firestore/cloud_firestore.dart';
import 'package:flutter/material.dart';
import 'package:firebase_auth/firebase_auth.dart';

class ChatScreen extends StatefulWidget {
  const ChatScreen({super.key});
  static const String screenRoute = "chat_screen";

  @override
  State<ChatScreen> createState() => _ChatScreenState();
}

class _ChatScreenState extends State<ChatScreen> {
  final _fireStore = FirebaseFirestore.instance;
  final _auth = FirebaseAuth.instance;
  late User signInUser;
  String? messageText;

  @override
  void initState() {
    super.initState();
    getCurrentUser();
  }

  void getCurrentUser() {
    try {
      final user = _auth.currentUser;
      if (user != null) {
        signInUser = user;
        print(signInUser.email);
      }
    } catch (e) {
      print(e);
    }
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        backgroundColor: Colors.orange,
        title: Text(
          "messages",
        ),
        actions: [
          IconButton(
              onPressed: () {
                _auth.signOut();
                Navigator.pop(context);
              },
              icon: Icon(Icons.close)),
        ],
      ),
      body: SafeArea(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.end,
          children: [
            Container(
              padding: EdgeInsets.only(left: 5),
              child: Row(
                children: [
                  Expanded(
                    child: TextField(
                      onChanged: (value) {
                        messageText = value;
                      },
                      decoration: InputDecoration(
                        hintText: "Write your message here...",
                        hintStyle: TextStyle(fontSize: 22),
                      ),
                    ),
                  ),
                  TextButton(
                    onPressed: () {
                      _fireStore.collection("message").add({
                        "name": messageText,
                        "email": signInUser.email,
                      });
                    },
                    child: Text(
                      "Send",
                      style: TextStyle(fontSize: 20),
                    ),
                  ),
                ],
              ),
            ),
          ],
        ),
      ),
    );
  }
}

this is image for my collection that i made it to get the messages
and this is the rules in Cloud Firestore Rules section

rules_version = '2';

service cloud.firestore {
  match /databases/{database}/documents {
    match /messages/{document} {
      allow read, write: if true;
    }
  }
}