Cannot start a service from another application with "not found" error

There are two apps, first one has a service and can start it. Second one tries to start the service from the first app and cannot because the service is "not found". I believe that the service is enabled and exported (see code below). What's wrong?

The manifest of the first app with declaration of the service:

<manifest ...
    package="com.example.fooapplication">

    <uses-permission android:name="android.permission.FOREGROUND_SERVICE" />

    <application ...>
        <service
            android:name=".FooService"
            android:enabled="true"
            android:exported="true">
        </service>

        <activity android:name=".MainActivity" ...>
            ...
        </activity>
    </application>

</manifest>

From that application I can start the FooService by the following commands:

Intent intent = new Intent();
intent.setComponent(new ComponentName("com.example.fooapplication", "com.example.fooapplication.FooService"));
Log.d("happy", "FooApplication " + intent);
startService(intent);

It works, there is the log (two last lines are from the service itself):

12-19 10:18:58.520 12869 12869 D happy   : FooApplication Intent { cmp=com.example.fooapplication/.FooService }
12-19 10:18:58.568 12869 12869 D happy   : FooService constructor
12-19 10:18:58.568 12869 12869 D happy   : FooService onCreate

The same code sequence at the second app cannot start that service:

12-19 10:31:22.300 13644 13644 D happy   : BarApplication Intent { cmp=com.example.fooapplication/.FooService }
12-19 10:31:22.301  1712  3872 W ActivityManager: Unable to start service Intent { cmp=com.example.fooapplication/.FooService } U=0: not found

Building parameters for both applications are:

compileSdkVersion 30
buildToolsVersion "30.0.0"
minSdkVersion 23
targetSdkVersion 30

Device with Android 12 (SDK 31)