Fixes a dispatcher bug that loses background processing state if jobs were submitted before ReplaceImplementation (#21735)

src/Avalonia.Base/Threading/Dispatcher.cs

@@ -162,6 +162,9 @@ public partial class Dispatcher : IDispatcher
             _backgroundProcessingImpl.ReadyForBackgroundProcessing += OnReadyForExplicitBackgroundProcessing;
         if (_signaled)
             _impl.Signal();
+        if (_explicitBackgroundProcessingRequested) 
+            _backgroundProcessingImpl?.RequestBackgroundProcessing();
+            
         _osTimerSetTo = null;
         UpdateOSTimer();
     }

tests/Avalonia.Base.UnitTests/DispatcherTests.cs

@@ -151,6 +151,38 @@ public partial class DispatcherTests
         Assert.Equal(new[] { "PromotedRender", "PromotedRender2", "Render" }, actions);
     }
 
+    [Fact]
+    public void DispatcherRepeatsBackgroundProcessingRequestToTheNewImplementation()
+    {
+        var actions = new List<string>();
+
+        // Requests background processing from the pre-initialization implementation
+        _uiThread.Post(() => actions.Add("Background"), DispatcherPriority.Background);
+
+        var impl = new SimpleDispatcherWithBackgroundProcessingImpl();
+        Dispatcher.InitializeUIThreadDispatcher(impl);
+
+        Assert.True(impl.AskedForBackgroundProcessing);
+        impl.FireBackgroundProcessing();
+        Assert.Equal(new[] { "Background" }, actions);
+    }
+
+    [Fact]
+    public void DispatcherRepeatsSignalToTheNewImplementation()
+    {
+        var actions = new List<string>();
+
+        // Signals the pre-initialization implementation
+        _uiThread.Post(() => actions.Add("Render"), DispatcherPriority.Render);
+
+        var impl = new SimpleDispatcherWithBackgroundProcessingImpl();
+        Dispatcher.InitializeUIThreadDispatcher(impl);
+
+        Assert.True(impl.AskedForSignal);
+        impl.ExecuteSignal();
+        Assert.Equal(new[] { "Render" }, actions);
+    }
+
     [Fact]
     public void DispatcherStopsItemProcessingWhenInteractivityDeadlineIsReached()
     {