Toolbar menu item with animation for notifications counter using Action View. Sample project: https://github.com/diegohkd/AndroidKotlinLab/tree/master/ToolbarMenuItemWithAnimation

action_view_notifications.xml

<?xml version="1.0" encoding="utf-8"?>
<example.com.toolbarmenuitemwithanimation.NotificationsActionView xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    style="?attr/actionButtonStyle"
    android:layout_width="match_parent"
    android:layout_height="match_parent">

    <ImageView
        android:id="@+id/bellImageView"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_marginEnd="8dp"
        android:src="@drawable/ic_notifications"
        app:layout_constraintBottom_toBottomOf="parent"
        app:layout_constraintEnd_toEndOf="parent"
        app:layout_constraintHorizontal_bias="0"
        app:layout_constraintStart_toStartOf="parent"
        app:layout_constraintTop_toTopOf="parent" />

    <TextView
        android:id="@+id/notificationsTextView"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_marginTop="4dp"
        android:background="@drawable/round_corners_background"
        android:ellipsize="end"
        android:maxLines="1"
        android:paddingStart="4dp"
        android:paddingEnd="4dp"
        android:textColor="@color/white"
        android:visibility="gone"
        app:layout_constrainedWidth="true"
        app:layout_constraintEnd_toEndOf="parent"
        app:layout_constraintHorizontal_bias="1"
        app:layout_constraintStart_toStartOf="parent"
        app:layout_constraintTop_toTopOf="parent"
        app:layout_constraintWidth_max="wrap"
        tools:text="4"
        tools:visibility="visible" />

</example.com.toolbarmenuitemwithanimation.NotificationsActionView>

main_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/notification"
        app:actionLayout="@layout/action_view_notifications"
        android:title="@string/notifications"
        app:showAsAction="always" />

</menu>

MainActivity.kt

class MainActivity : AppCompatActivity() {
    ...
    private var notificationsActionView: NotificationsActionView? = null
    ...
    override fun onCreateOptionsMenu(menu: Menu): Boolean {
        menuInflater.inflate(R.menu.main_menu, menu)
        return true
    }

    override fun onPrepareOptionsMenu(menu: Menu?): Boolean {
        val notificationItem = menu?.findItem(R.id.notification)?.actionView
        notificationsActionView = notificationItem as? NotificationsActionView
        notificationsActionView?.setOnClickListener {
            Toast.makeText(this, "Not implemented", Toast.LENGTH_SHORT).show()
        }
        return super.onPrepareOptionsMenu(menu)
    }
}

NotificationsActionView.kt

class NotificationsActionView(
    context: Context, attrs: AttributeSet? = null
) : ConstraintLayout(context, attrs) {
    
    private val bounceAnimation: Animation by lazy {
        AnimationUtils.loadAnimation(context, R.anim.bounce_interpolar)
    }

    fun setNotificationsCount(count: Int) {
        if (count <= 0) {
            notificationsTextView.text = ""
            notificationsTextView.isVisible = false
        } else {
            notificationsTextView.text = if (count > 99) {
                resources.getString(R.string.max_count_plus)
            } else {
                count.toString()
            }
            notificationsTextView.isVisible = true
            notificationsTextView.startAnimation(bounceAnimation)
        }
    }
}