Fix: IsBackground derived from SourceType + per-scene background property tests

- Source.Type setter auto-sets IsBackground = true when Type is Background
- SceneElement.IsBackground: expression-bodied → virtual auto-property
- Source.IsBackground: new → override (WPF binding fix)
- Three new tests: IsBackground per-scene, derived from type, UseDefaultBackground default

Models/Source.cs

@@ -37,6 +37,7 @@ public class Source : SceneElement
         {
             if (Set(ref _type, value))
             {
+                IsBackground = value == SourceType.Background;
                 Raise(nameof(IsLiveCapture));
                 Raise(nameof(DisplaySource));
                 Raise(nameof(IsWebSource));

ytLive.Tests/BackgroundTests.cs

@@ -122,4 +122,42 @@ public class BackgroundTests
         Assert.Contains(nameof(Source.IsLiveCapture), raised);
         Assert.Contains(nameof(Source.DisplaySource), raised);
     }
+
+    [Fact]
+    public void AllScenes_BackgroundElement_HasIsBackgroundTrue()
+    {
+        foreach (var name in SceneCatalog.All)
+        {
+            var scene = new Scene { Name = name, HasBackground = SceneCatalog.HasBackground(name) };
+            var bg = new Source { Name = "Background", Type = SourceType.Background };
+            scene.Elements.Add(bg);
+
+            Assert.True(bg.IsBackground,
+                $"{name}: Background element must have IsBackground = true for properties panel");
+        }
+    }
+
+    [Fact]
+    public void AllScenes_BackgroundElement_IsBackgroundDerivedFromType()
+    {
+        var bg = new Source { Type = SourceType.Background };
+        Assert.True(bg.IsBackground);
+
+        var nonBg = new Source { Type = SourceType.Image };
+        Assert.False(nonBg.IsBackground);
+
+        var display = new Source { Type = SourceType.DisplayCapture };
+        Assert.False(display.IsBackground);
+    }
+
+    [Fact]
+    public void AllScenes_BackgroundElement_SupportsUseDefaultBackground()
+    {
+        foreach (var name in SceneCatalog.All)
+        {
+            var scene = new Scene { Name = name };
+            Assert.True(scene.UseDefaultBackground,
+                $"{name}: Scene must default to UseDefaultBackground = true");
+        }
+    }
 }