Set OverlayInputPassThroughElement in MenuItem template.

src/Avalonia.Controls/Menu.cs

@@ -48,13 +48,6 @@ namespace Avalonia.Controls
                 return;
             }
 
-            if (_overlay?.InputPassThroughElement == this)
-            {
-                _overlay.InputPassThroughElement = null;
-            }
-
-            _overlay = null;
-
             foreach (var i in ((IMenu)this).SubItems)
             {
                 i.Close();
@@ -78,13 +71,6 @@ namespace Avalonia.Controls
                 return;
             }
 
-            _overlay = LightDismissOverlayLayer.GetLightDismissOverlayLayer(this);
-
-            if (_overlay is object)
-            {
-                _overlay.InputPassThroughElement = this;
-            }
-
             IsOpen = true;
 
             RaiseEvent(new RoutedEventArgs

src/Avalonia.Themes.Fluent/MenuItem.xaml

@@ -161,7 +161,8 @@
                    WindowManagerAddShadowHint="False"
                    MinWidth="{Binding Bounds.Width, RelativeSource={RelativeSource TemplatedParent}}"
                    IsLightDismissEnabled="True"
-                   IsOpen="{TemplateBinding IsSubMenuOpen, Mode=TwoWay}">
+                   IsOpen="{TemplateBinding IsSubMenuOpen, Mode=TwoWay}"
+                   OverlayInputPassThroughElement="{Binding $parent[Menu]}">
               <Border Background="{DynamicResource MenuFlyoutPresenterBackground}"
                       BorderBrush="{DynamicResource MenuFlyoutPresenterBorderBrush}"
                       BorderThickness="{DynamicResource MenuFlyoutPresenterBorderThemeThickness}"