Bubble exceptions out of publishers.

src/Aspire.Hosting/DistributedApplicationRunner.cs

@@ -74,7 +74,7 @@ await activityReporter.UpdateActivityStatusAsync(
 
                 if (!backchannelService.IsBackchannelExpected)
                 {
-                     lifetime.StopApplication();
+                     throw new DistributedApplicationException($"Publishing failed exception message: {ex.Message}", ex);
                 }
             }
         }

tests/Aspire.Hosting.Tests/DistributedApplicationRunnerTests.cs

@@ -0,0 +1,41 @@
+// Licensed to the .NET Foundation under one or more agreements.
+// The .NET Foundation licenses this file to you under the MIT license.
+
+using Aspire.Hosting.Publishing;
+using Aspire.Hosting.Utils;
+using Xunit;
+
+namespace Aspire.Hosting.Tests;
+
+public class DistributedApplicationRunnerTests(ITestOutputHelper outputHelper)
+{
+    [Fact]
+    public void EnsureFailingPublishResultsInRunMethodThrowing()
+    {
+        var args = new[] { "--publisher", "explodingpublisher" };
+        using var builder = TestDistributedApplicationBuilder.Create(outputHelper, args);
+#pragma warning disable ASPIREPUBLISHERS001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
+        builder.AddPublisher<ExplodingPublisher, ExplodingPublisherOptions>("explodingpublisher");
+#pragma warning restore ASPIREPUBLISHERS001 // Type is for evaluation purposes only and is subject to change or removal in future updates. Suppress this diagnostic to proceed.
+        using var app = builder.Build();
+
+        var ex = Assert.Throws<AggregateException>(app.Run);
+
+        Assert.Collection(
+            ex.InnerExceptions,
+            e => Assert.Equal("Publishing failed exception message: Boom!", e.Message)
+        );
+    }
+}
+
+internal sealed class ExplodingPublisher : IDistributedApplicationPublisher
+{
+    public Task PublishAsync(DistributedApplicationModel model, CancellationToken cancellationToken)
+    {
+        throw new NotImplementedException("Boom!");
+    }
+}
+
+internal sealed class ExplodingPublisherOptions
+{
+}