Treeview control and setting individual items to checked

<Grid RowDefinitions="*,*">
    <telerik:RadTreeView x:Name="treeView" 
                        ItemsSource="{Binding Items}"
                            CheckedItems="{Binding Checked}"
                        CheckBoxMode="Recursive">
        <telerik:TreeViewDescriptor ItemsSourcePath="Children" DisplayMemberPath="Name"
                                TargetType="{x:Type local:Item}"/>
    </telerik:RadTreeView>
    <telerik:RadListView Grid.Row="1" x:Name="list" ItemsSource="{Binding CheckedItems, Source={x:Reference treeView}}"/>
</Grid>

<?xml version="1.0" encoding="utf-8" ?>
<ContentPage xmlns="http://schemas.microsoft.com/dotnet/2021/maui"
             xmlns:x="http://schemas.microsoft.com/winfx/2009/xaml"
             xmlns:telerik="http://schemas.telerik.com/2022/xaml/maui"
             xmlns:local="clr-namespace:InterfaceAdminToolV2.ViewModel"
			 x:DataType="local:MainPageViewModel"
             x:Class="InterfaceAdminToolV2.View.MainPage">

	<VerticalStackLayout Spacing="30">
		<telerik:RadTreeView x:Name="treeView"
							 HeightRequest="500"
							 ItemsSource="{Binding Items}"
							 CheckBoxMode="Recursive"
							 CheckedItems="{Binding CheckedItems, Mode=TwoWay}">

			<telerik:TreeViewDescriptor TargetType="{x:Type local:Item}"
			                            DisplayMemberPath="Name"
			                            ItemsSourcePath="Children" />
		</telerik:RadTreeView>

		<!-- control just to debug to see what has been checked-->
		<telerik:RadTreeView x:Name="checkedTree"
		                     HeightRequest="500"
		                     ItemsSource="{Binding CheckedItems, Source={x:Reference treeView}}"
		                     CheckBoxMode="Recursive">

			<telerik:TreeViewDescriptor TargetType="{x:Type local:Item}"
			                            DisplayMemberPath="Name"
			                            ItemsSourcePath="Children" />
		</telerik:RadTreeView>
	</VerticalStackLayout>
</ContentPage>

using System.Collections.ObjectModel;
namespace InterfaceAdminToolV2.ViewModel;

public partial class MainPageViewModel : ViewModelBase
{
    [ObservableProperty]
    private ObservableCollection<Item> items;

    [ObservableProperty]
    private ObservableCollection<Item> checkedItems;

    public MainPageViewModel()
    {
        Items = new ObservableCollection<Item>();
        Items.Add(new Item
        {
            Name = "My Projects",
            Children = new List<Item>()
            {
                new Item()
                {
                    Name = "Using latest Telerik .NET MAUI controls",
                    Children = new ObservableCollection<Item>()
                    {
                        new Item { Name = "TreeView"},
                        new Item() {Name = "Calendar"},
                        new Item() {Name = "RichTextEditor"},
                        new Item(){Name = "PdfViewer"},
                        new Item(){Name = "SlideView"},
                        new Item() {Name = "Chat"},
                    }
                },
                new Item { Name = "Blank project" }
            }
        });
        Items.Add(new Item()
        {
            Name = "Shared Documents",
            Children = new List<Item>()
            {
                new Item()
                {
                    Name = "Reports",
                    Children = new List<Item>()
                    {
                        new Item(){Name = "October"},
                        new Item() {Name = "November"},
                        new Item(){Name = "December"}
                    }
                }
            }
        });

        var existingSelectedItems = Items.SkipLast(1).ToList();
        CheckedItems = new ObservableCollection<Item>(existingSelectedItems);
    }
}

public class Item
{
    public string Name { get; set; }
    public IList<Item> Children { get; set; } = new List<Item>();

    public bool HasChildren => Children.Any();
}

<?xml version="1.0" encoding="utf-8"?>

<ContentPage xmlns="http://schemas.microsoft.com/dotnet/2021/maui"
             xmlns:x="http://schemas.microsoft.com/winfx/2009/xaml"
             xmlns:telerik="http://schemas.telerik.com/2022/xaml/maui"
			 xmlns:viewmodel="clr-namespace:InterfaceAdminToolV2.ViewModel"
			 x:Class="InterfaceAdminToolV2.View.DropDownPage"
             x:DataType="viewmodel:DropDownPageViewModel">

	<Grid RowDefinitions="Auto,*, *">
		

		<telerik:RadTreeView x:Name="treeView" Grid.Row="1"
		                     AutomationId="treeView" 
							 SelectionMode="None"
		                     ItemsSource="{Binding Books}"
							 CheckBoxMode="Independent"
		                     CheckedItems="{Binding CheckedItems}">

			<telerik:TreeViewDescriptor DisplayMemberPath="Title"
			                            ItemsSourcePath="Authors"
			                            TargetType="{x:Type viewmodel:Book}" />
		</telerik:RadTreeView>
		<VerticalStackLayout Grid.Row="2">
			<Label Text="CheckedItem's collection" />
			<telerik:RadListView  ItemsSource="{Binding CheckedItems}">
				<telerik:RadListView.ItemTemplate>
					<DataTemplate>
						<telerik:ListViewTextCell x:DataType="viewmodel:Book" Text="{Binding Id}"
						                          Detail="{Binding Title}"
						                          TextColor="Black"
						                          DetailColor="Gray" />
					</DataTemplate>
				</telerik:RadListView.ItemTemplate>
			</telerik:RadListView>
		</VerticalStackLayout>
	</Grid>

</ContentPage>

using System.Collections.ObjectModel;
using Telerik.Maui.Controls;

namespace InterfaceAdminToolV2.ViewModel;

public partial class DropDownPageViewModel : NotifyPropertyChangedBase
{
    public DropDownPageViewModel()
    {
        Books = new ObservableCollection<Book>();

        Books.Add(new Book(1, "First Book")
        {
            Authors = new List<Book>
        {
            new Book(99, "Sam Dob"),
            new Book(23, "Mark Semt")
        }
        }
        );
        
        Books.Add(new Book(2, "Shared Documents"));
        Initialize();
    }

    private void Initialize()
    {
        CheckedItems = new ObservableCollection<Book>();

        foreach (var node in Books)
        {
            CheckedItems.Add(node);

            foreach (var nodeAuthor in node.Authors)
            {
                    CheckedItems.Add(nodeAuthor);
            }
        }

    }

    private ObservableCollection<Book> checkedItems;

    public ObservableCollection<Book> CheckedItems
    {
        get => this.checkedItems;
        set
        {
            if (this.checkedItems != value)
            {
                this.checkedItems = value;
                this.OnPropertyChanged();
            }
        }
    }
    public ObservableCollection<Book> Books { get; set; }
}

public class Book
{
    public Book(int id, string title)
    {
        this.Id = id; this.Title = title;
        this.Authors = new List<Book>();
    }

    public int Id { get; set; }
    public string Title { get; set; }
    public IList<Book> Authors { get; set; }
}