x:Name attribute inside a DataTemplate does not directly associate the named element with the CollectionView’s FindByName method. Each item in the CollectionView has its own DataTemplate. So your approach won’t work.

If Manipulating properties of HorizontalStackLayout is you goal, Then you need to find another way.

One Way is to create new properties in you model class and bind them to the property you want to manipulate when selection changed.

public class Item
{
   public string title;
   public Color ItemBackgroundColor = Colors.Red; // new property in model class
}

in xaml bind it

 <DataTemplate>
     <HorizontalStackLayout BackgroundColor={Binding ItemBackgroundColor} x:Name="horizontalStackLayout ">
        <Label
            Text="{Binding title}" />
     </HorizontalStackLayout>
</DataTemplate>

Now you can set the property in SelectionChanged event

private async void OnItemSelected(object sender, SelectionChangedEventArgs e)
{
    foreach(var selectedItem in e.CurrentSelection)
    {
        if(selectedItem is Item _item)
        {
           _item.ItemBackgroundColor = Colors.Green;
        }
     }
}

Note: Make sure changes in model properties are notified to view.

One of the easier ways to react to a selection in CollectionView is to bind the SelectedItem property. I kludged a CollectionView onto the MAUI default as a minimal example of doing this.

<CollectionView 
    MinimumHeightRequest="400"
    BackgroundColor="Azure"
    SelectionMode="Single"
    ItemsSource="{Binding items}"
    SelectedItem="{Binding SelectedItem}">
    <CollectionView.ItemsLayout>
        <LinearItemsLayout Orientation="Vertical" ItemSpacing="1" />
    </CollectionView.ItemsLayout>
    <CollectionView.ItemTemplate>
        <DataTemplate>
            <Frame 
                Margin="10"
                Padding="10"
                BackgroundColor="White"
                CornerRadius="10"
                HasShadow="True"
                InputTransparent="true">
                <HorizontalStackLayout>
                    <Label 
                        Text="{Binding title}" 
                        FontSize="16"
                        FontAttributes="Bold"
                        TextColor="Black" />
                </HorizontalStackLayout>
            </Frame>
        </DataTemplate>
    </CollectionView.ItemTemplate>
</CollectionView>

Binding context for MainPage

class MainPageBindingContext : INotifyPropertyChanged
{
    public ObservableCollection<Item> items { get; } = new ObservableCollection<Item>
    {
        new Item{title = "Item A"},
        new Item{title = "Item B"},
    };

    // Because we're in "single" mode, we bind SelectedItem, not SelectedItems
    public Item? SelectedItem
    {
        get => _selectedItem;
        set
        {
            if (!Equals(_selectedItem, value))
            {
                _selectedItem = value;
                OnPropertyChanged();
                // Quick and dirty. You will want to improve on this.
                foreach (var item in items)
                {
                    if(ReferenceEquals(_selectedItem, item))
                    {
                        item.title = $"{item.title} SELECTED";
                    }
                    else
                    {
                        item.title = item.title.Replace(" SELECTED", string.Empty);
                    }
                }
            }
        }
    }
    Item? _selectedItem = default;

    protected virtual void OnPropertyChanged([CallerMemberName] string? propertyName = null) => 
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));

    public event PropertyChangedEventHandler? PropertyChanged;
}

Binding context for Item

class Item : INotifyPropertyChanged
{
    public string title
    {
        get => _title;
        set
        {
            if (!Equals(_title, value))
            {
                _title = value;
                OnPropertyChanged();
            }
        }
    }
    string _title = "{New Item}";
    protected virtual void OnPropertyChanged([CallerMemberName] string? propertyName = null) =>
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
    public event PropertyChangedEventHandler? PropertyChanged;
}