Uncaught ReferenceError: firebase is not definedというエラーが出る

firebaseを使ってウェブチャットを作りたい。

var database = firebase.database();でエラーが出ます。

<!DOCTYPE html>
<html lang="ja">
<head>
    <meta charset="UTF-8">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>webchat</title>
</head>
<body>


    <div>
        <div>
            <input type="text" id="name">
        </div>
        <div>
             <textarea id="message" row="10"></textarea>
             <button id="send">send</button>
        </div>
        <div id="output"></div>
    </div>
    

    <script type="module">
        // Import the functions you need from the SDKs you need
        import { initializeApp } from "https://www.gstatic.com/firebasejs/9.8.1/firebase-app.js";
        import { getAnalytics } from "https://www.gstatic.com/firebasejs/9.8.1/firebase-analytics.js";
        // TODO: Add SDKs for Firebase products that you want to use
        // https://firebase.google.com/docs/web/setup#available-libraries
      
        // Your web app's Firebase configuration
        // For Firebase JS SDK v7.20.0 and later, measurementId is optional
        const firebaseConfig = {
          apiKey: "AIzaSyCBZkDxfPA4F5T8yFN6nRN13cxXO13onl0",
          authDomain: "chat-e82eb.firebaseapp.com",
          projectId: "chat-e82eb",
          storageBucket: "chat-e82eb.appspot.com",
          messagingSenderId: "506878072817",
          appId: "1:506878072817:web:6c2b7abfeea16350209650",
          measurementId: "G-CTE5H5HRTT"
        };
      
        // Initialize Firebase
        const app = initializeApp(firebaseConfig);
        const analytics = getAnalytics(app);
      </script>
      <script src="javascript/webchat.js"></script>
</body>
</html>


**webchat.js**
{
    var database = firebase.database();
        let room = "chat_room";
        const send = document.getElementById("send");
        const name = document.getElementById("name");
        const message = document.getElementById("message");
        const output = document.getElementById("output");

        send.addEventListener('click', function() {
            database.ref(room).push({
                name:name.value,
                message:message.value
            });
            message.value="";
            name.value="";
        });

        database.ref(room).on("child_added", function(data) {
            const v = data.val();
            const k = data.key;
            let str = "";
            str += '<div class="name">名前：'+v.name+'</div>';
            str += '<div class="text">メッセージ：'+v.message+'</div>';
            output.innerHTML += str;
        });
}