Improve code around background screen handling to read better

osu.Game/Screens/BackgroundScreenStack.cs

@@ -17,15 +17,21 @@ public BackgroundScreenStack()
             Origin = Anchor.Centre;
         }
 
-        public void Push(BackgroundScreen screen)
+        /// <summary>
+        /// Attempt to push a new background screen to this stack.
+        /// </summary>
+        /// <param name="screen">The screen to attempt to push.</param>
+        /// <returns>Whether the push succeeded. For example, if the existing screen was already of the correct type this will return <c>false</c>.</returns>
+        public bool Push(BackgroundScreen screen)
         {
             if (screen == null)
-                return;
+                return false;
 
             if (EqualityComparer<BackgroundScreen>.Default.Equals((BackgroundScreen)CurrentScreen, screen))
-                return;
+                return false;
 
             base.Push(screen);
+            return true;
         }
     }
 }

osu.Game/Screens/OsuScreen.cs

@@ -186,17 +186,14 @@ public override void OnEntering(IScreen last)
         {
             applyArrivingDefaults(false);
 
-            backgroundStack?.Push(ownedBackground = CreateBackground());
+            if (backgroundStack?.Push(ownedBackground = CreateBackground()) != true)
-
-            background = backgroundStack?.CurrentScreen as BackgroundScreen;
-
-            if (background != ownedBackground)
             {
-                // background may have not been replaced, at which point we don't want to track the background lifetime.
+                // If the constructed instance was not actually pushed to the background stack, we don't want to track it unnecessarily.
                 ownedBackground?.Dispose();
                 ownedBackground = null;
             }
 
+            background = backgroundStack?.CurrentScreen as BackgroundScreen;
             base.OnEntering(last);
         }