How to change the Background property of a selected TreeViewItem using Styles/Triggers

Hi,
you can use Trigger in ItemContainerStyle like in following demo:

<Window x:Class="Window085"  
        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:WpfApp1.WpfApp085"  
        mc:Ignorable="d"  
        Title="Window085" Height="450" Width="800">  
  <Window.DataContext>  
    <local:ViewModel/>  
  </Window.DataContext>  
  <Grid>  
    <TreeView ItemsSource="{Binding View}">  
      <TreeView.ItemContainerStyle>  
        <Style TargetType="{x:Type TreeViewItem}">  
          <Setter Property="IsExpanded" Value="{Binding IsExpanded, Mode=TwoWay}" />  
          <Setter Property="Background" Value="Transparent"/>  
          <Style.Triggers>  
            <DataTrigger Binding="{Binding IsSelected}" Value="True">  
              <Setter Property="Background" Value="Yellow"/>  
            </DataTrigger>  
          </Style.Triggers>  
        </Style>  
      </TreeView.ItemContainerStyle>  
      <TreeView.ItemTemplate>  
        <HierarchicalDataTemplate ItemsSource="{Binding Children}">  
          <StackPanel Orientation="Horizontal">  
            <TextBlock VerticalAlignment="Center" Text="{Binding Name}" />  
          </StackPanel>  
        </HierarchicalDataTemplate>  
      </TreeView.ItemTemplate>  
    </TreeView>  
  </Grid>  
</Window>  

And ViewModel:

Imports System.Collections.ObjectModel  
Imports System.ComponentModel  
  
Namespace WpfApp085  
  Public Class ViewModel  
  
    Private ReadOnly col As New ObservableCollection(Of Data)  
    Private ReadOnly cvs As New CollectionViewSource  
  
    Public ReadOnly Property View As ICollectionView  
      Get  
        If cvs.Source Is Nothing Then GetData()  
        Return cvs.View  
      End Get  
    End Property  
  
    Private Sub GetData()  
      Dim rnd As New Random  
      For i = 1 To 100  
        Dim d As New Data With {.Name = $"Node {i}", .IsSelected = rnd.NextDouble > 0.5}  
        For k = 1 To 10  
          d.Children.Add(New Data With {.Name = $"Node {i} {k}", .IsSelected = rnd.NextDouble > 0.5})  
        Next  
        col.Add(d)  
      Next  
      cvs.Source = col  
    End Sub  
  End Class  
  
  Public Class Data  
    Public Property Name As String  
    Public Property IsExpanded As Boolean = True  
    Public Property IsSelected As Boolean  
    Public Property Children As New ObservableCollection(Of Data)  
  End Class  
  
End Namespace  

Result: