API 31, android 12 and android:exported="true"

Question

I have a big problem, i had an android application with flutter since two or three years, and i just want to correct a little bug. It's perfectly working in my computer but when i want to upload the new release in the playstore it's tell me that i have to upgrade the API cible at 31. I have do this but after it tell me a new error :

You uploaded an APK or Android App Bundle which has an activity, activity alias, service or broadcast receiver with intent filter, but without 'android:exported' property set. This file can't be installed on Android 12 or higher. See: developer.android.com/about/versions/12/behavior-changes-12#exported

I'm looking for an easy solution since this morning, but with no success.. i read that i have to add this code android:exported="true" but after that i have the same problem...

this is my AndroidManifest.xml :

<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="com.my.App_app">
    <!-- io.flutter.app.FlutterApplication is an android.app.Application that
         calls FlutterMain.startInitialization(this); in its onCreate method.
         In most cases you can leave this as-is, but you if you want to provide
         additional functionality it is fine to subclass or reimplement
         FlutterApplication and put your custom class here. -->
    <application
        android:name="io.flutter.app.FlutterApplication"
        android:label="App Label"
        android:icon="@mipmap/ic_launcher">
        <activity
            android:name=".MainActivity"
            android:exported="true"
            android:launchMode="singleTop"
            android:theme="@style/LaunchTheme"
            android:configChanges="orientation|keyboardHidden|keyboard|screenSize|smallestScreenSize|locale|layoutDirection|fontScale|screenLayout|density|uiMode"
            android:hardwareAccelerated="true"
            android:windowSoftInputMode="adjustResize">
            <!-- Specifies an Android theme to apply to this Activity as soon as
                 the Android process has started. This theme is visible to the user
                 while the Flutter UI initializes. After that, this theme continues
                 to determine the Window background behind the Flutter UI. -->
            <meta-data
              android:name="io.flutter.embedding.android.NormalTheme"
              android:resource="@style/NormalTheme"
              />
            <!-- Displays an Android View that continues showing the launch screen
                 Drawable until Flutter paints its first frame, then this splash
                 screen fades out. A splash screen is useful to avoid any visual
                 gap between the end of Android's launch screen and the painting of
                 Flutter's first frame. -->
            <meta-data
              android:name="io.flutter.embedding.android.SplashScreenDrawable"
              android:resource="@drawable/launch_background"
              />
            <intent-filter>

                <action android:name="android.intent.action.MAIN"/>
                <category android:name="android.intent.category.LAUNCHER"/>
            </intent-filter>
        </activity>
        <meta-data
            android:name="com.google.firebase.messaging.default_notification_icon"
            android:resource="@mipmap/ic_launcher2" />
        <!-- Don't delete the meta-data below.
             This is used by the Flutter tool to generate GeneratedPluginRegistrant.java -->
        <meta-data
            android:name="flutterEmbedding"
            android:value="2" />
    </application>
</manifest>

Thanks in advance !