Binding not working when custom control is used in a datagridtemplatecolumn

public class OutputColumn : ObservableObject
{
    private string spaltenname;
    private bool isChecked;

    public string Spaltenname
    {
        get => spaltenname;
        set => Set(ref spaltenname, value);
    }

    public bool IsChecked
    {
        get => isChecked;
        set => Set(ref isChecked, value);
    }

    public ObservableCollectionEx<Tag> Tags { get; set; }
}

public class Tag : ObservableObject
{
    private string name;
    private bool isChecked;

    public string Name
    {
        get => name;
        set => Set(ref name, value);
    }

    public bool IsChecked
    {
        get => isChecked;
        set => Set(ref isChecked, value);
    }
}

public class ObservableCollectionEx<T> : ObservableCollection<T> where T : INotifyPropertyChanged
{
    private int itemChangeCount;

    public int ItemChangeCount
    {
        get => itemChangeCount;
        set
        {
            itemChangeCount = value;
            OnPropertyChanged(new PropertyChangedEventArgs(nameof(ItemChangeCount)));
        }
    }

    protected override void OnCollectionChanged(NotifyCollectionChangedEventArgs e)
    {
        if (e.Action == NotifyCollectionChangedAction.Add)
        {
            foreach (T item in e.NewItems!.Cast<T>())
            {
                item.PropertyChanged += Item_PropertyChanged;
            }
        }
        if (e.Action == NotifyCollectionChangedAction.Remove)
        {
            foreach (T item in e.NewItems!.Cast<T>())
            {
                item.PropertyChanged -= Item_PropertyChanged;
            }
        }
    }

    private void Item_PropertyChanged(object? sender, PropertyChangedEventArgs e)
    {
        ItemChangeCount += 1;
    }
}

public abstract class ObservableObject : INotifyPropertyChanged
{
    public void Set<TValue>(ref TValue field, TValue newValue, [CallerMemberName] string propertyName = "")
    {
        if (!EqualityComparer<TValue>.Default.Equals(field, default) && field!.Equals(newValue))
            return;

        field = newValue;
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
    }

    public event PropertyChangedEventHandler? PropertyChanged;
}

public class SummaryConverter : IMultiValueConverter
{
    public object? Convert(
        object[] values, 
        Type targetType, 
        object parameter, 
        CultureInfo culture)
    {
        if (values.Length < 2)
            return null;

        if (values
            .Any(x => x == DependencyProperty.UnsetValue))
            return null;

        bool isChecked = (bool)values[0];
        IEnumerable<Tag> TagItems = (IList<Tag>)values[1];

        List<string> tags = new()
            { isChecked
                ? "checked "
                : "unchecked " };

        tags.AddRange(TagItems
            .Where(tag => tag.IsChecked)
            .Select(tag => tag.Name));

        return string.Join(", ", tags);
    }

    public object[] ConvertBack(
        object value,
        Type[] targetTypes,
        object parameter,
        CultureInfo culture)
        => throw new NotImplementedException();
}

public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
        InitData();
    }

    private Random random = new();

    public ObservableCollection<OutputColumn> OutputColumns { get; set; }
        = new();

    void InitData()
    {
        for (int i = 0; i < 10; i++)
        {
            OutputColumn item = new()
            {
                Spaltenname = $"Item {i + 1}",
                IsChecked = random.Next(0, 2) == 1,
                Tags = new()
                {
                    new()
                    {
                        Name = "Asset Type",
                        IsChecked = random.Next(0, 2) == 1
                    },
                    new()
                    {
                        Name = "Service Tag",
                        IsChecked = random.Next(0, 2) == 1
                    },
                    new()
                    {
                        Name = "Item Number",
                        IsChecked = random.Next(0, 2) == 1
                    },
                    new()
                    {
                        Name = "System Brand",
                        IsChecked = random.Next(0, 2) == 1
                    },
                    new()
                    {
                        Name = "Description",
                        IsChecked = random.Next(0, 2) == 1
                    },
                }
            };

            OutputColumns.Add(item);
        }
    }
}

<Window x:Class="WpfDataGridComboBoxColumn.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:WpfDataGridComboBoxColumn"
        mc:Ignorable="d"
        x:Name="Window"
        Title="MainWindow" Height="450" Width="800">
    <DataGrid x:Name="DataGrid" ItemsSource="{Binding ElementName=Window, Path=OutputColumns}"
              AutoGenerateColumns="False">
        <DataGrid.Resources>
            <local:SummaryConverter x:Key="StaticSummaryConverter" />
        </DataGrid.Resources>
        <DataGrid.Columns>
            <DataGridCheckBoxColumn
                Binding="{
                    Binding IsChecked,
                    UpdateSourceTrigger=PropertyChanged}"
                Header="IsChecked"/>
            <DataGridTextColumn Binding="{Binding Spaltenname}"
                                Header="Name"/>
            <DataGridTemplateColumn Header="AdditionsSpalten">
                <DataGridTemplateColumn.CellTemplate>
                    <DataTemplate>
                        <ComboBox
                            ItemsSource="{Binding Path=Tags}"
                                                  DisplayMemberPath="Name">
                            <ComboBox.ItemTemplate>
                                <DataTemplate>
                                    <StackPanel Orientation="Horizontal">
                                        <CheckBox 
                                            IsChecked="{Binding IsChecked,
                                                UpdateSourceTrigger=PropertyChanged}" />
                                        <TextBlock Text="{Binding Name}" />
                                    </StackPanel>
                                </DataTemplate>
                            </ComboBox.ItemTemplate>
                        </ComboBox> 

                    </DataTemplate>
                </DataGridTemplateColumn.CellTemplate>
            </DataGridTemplateColumn>
            <DataGridTemplateColumn Header="Summary">
                <DataGridTemplateColumn.CellTemplate>
                    <DataTemplate>
                        <TextBlock>
                            <TextBlock.Text>    
                                <MultiBinding
                                    Converter="{StaticResource StaticSummaryConverter}">
                                    <Binding Path="IsChecked" />
                                    <Binding Path="Tags"/>
                                    <Binding Path="Tags.ItemChangeCount"/>
                                </MultiBinding>
                            </TextBlock.Text>
                        </TextBlock>
                    </DataTemplate>
                </DataGridTemplateColumn.CellTemplate>
            </DataGridTemplateColumn>
        </DataGrid.Columns>

    </DataGrid>
</Window>