Android MaterialToolbar what is app:menu used for?

Question

I'm developing an android app in Java and want to add a custom regular MaterialToolbar with a settings icon on the right side.
I had a look at the MDC-Android how to implement it.
In the Android Studio design preview everything looked just fine, but when I ran the app on the emulator, the AppBar showed up without the custom menu (settings icon).

My AppBarLayout:

<com.google.android.material.appbar.AppBarLayout
    ...
    >

    <com.google.android.material.appbar.MaterialToolbar
        android:id="@+id/topAppBar"
        android:layout_width="match_parent"
        android:layout_height="?attr/actionBarSize"
        app:menu="@menu/custom_menu"
        app:title="@string/app_name" />

</com.google.android.material.appbar.AppBarLayout>

custom_menu.xml

<?xml version="1.0" encoding="utf-8"?>
<menu xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto">
    <item
        android:id="@+id/nav_settings"
        android:contentDescription="@string/settings_description"
        android:icon="@drawable/ic_baseline_settings_24"
        android:title="@string/settings"
        app:showAsAction="ifRoom" />
</menu>

After some time I figured out, that I still have to add following code to my AppCompatActivity, to actually show the custom menu (not only in the preview):

@Override
public boolean onCreateOptionsMenu(Menu menu) {
    getMenuInflater().inflate(R.menu.custom_menu, menu);
    return super.onCreateOptionsMenu(menu);
}

I thought it would be enough to add the app:menu attribute to my MaterialToolbar, but it seems like it just affects the preview. (The running app also shows the custom menu if the app:menu attribute isn't used)
I couldn't find anything about what app:menu except for some related methods (Found here), but this didn't really help me.

Is the app:menu attribute just used for the Android Studio preview?
If yes => why isn't it in the tools namespace (tools:menu)
If no => what other use cases does app:menu have?