fix: stop adding topic and retain when writing an MQTT lastWill

LastWill wrote `topic` with WriteRequiredProperty and `retain` from a
non-nullable bool, so reading `lastWill: { qos: 1 }` and writing it back
produced `topic:` (null) and `retain: false`. Both fields are optional in
the MQTT binding spec.

`retain` now has a nullable backing field (same pattern as
MQTTOperationBinding), and both fields are written only when set. The
public `Retain` property keeps its bool type, so this is not a breaking
API change.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

Author: 2 people

src/ByteBard.AsyncAPI.Bindings/MQTT/LastWill.cs

@@ -6,6 +6,8 @@
 
     public class LastWill : IAsyncApiElement
     {
+        private bool? retain;
+
         /// <summary>
         /// The topic where the Last Will and Testament message will be sent.
         /// </summary>
@@ -26,7 +28,11 @@ public class LastWill : IAsyncApiElement
         /// <summary>
         /// Whether the broker should retain the Last Will and Testament message or not.
         /// </summary>
-        public bool Retain { get; set; }
+        public bool Retain
+        {
+            get => this.retain ?? false;
+            set => this.retain = value;
+        }
 
         public void Serialize(IAsyncApiWriter writer)
         {
@@ -36,10 +42,10 @@ public void Serialize(IAsyncApiWriter writer)
             }
 
             writer.WriteStartObject();
-            writer.WriteRequiredProperty("topic", this.Topic);
+            writer.WriteOptionalProperty("topic", this.Topic);
             writer.WriteOptionalProperty("qos", (int?)this.QoS);
             writer.WriteOptionalProperty("message", this.Message);
-            writer.WriteRequiredProperty("retain", this.Retain);
+            writer.WriteOptionalProperty("retain", this.retain);
             writer.WriteEndObject();
         }
     }

test/ByteBard.AsyncAPI.Tests/Bindings/MQTT/MQTTBindingVariants_Should.cs

@@ -111,5 +111,35 @@ public void OperationBinding_OmitsUnsetQosAndRetain()
             var yaml = new MQTTOperationBinding().SerializeAsYaml(AsyncApiVersion.AsyncApi3_0);
             yaml.Should().NotContain("qos:").And.NotContain("retain:");
         }
+
+        [TestCase(AsyncApiVersion.AsyncApi2_0)]
+        [TestCase(AsyncApiVersion.AsyncApi3_0)]
+        public void LastWill_WithoutTopicAndRetain_RoundTripsWithoutAddingThem(AsyncApiVersion version)
+        {
+            var settings = new AsyncApiReaderSettings { Bindings = BindingsCollection.MQTT };
+            var yaml = (version == AsyncApiVersion.AsyncApi2_0 ? "url" : "host") + ": localhost\n" +
+                """
+                protocol: mqtt
+                bindings:
+                  mqtt:
+                    lastWill:
+                      qos: 1
+                """;
+
+            var server = new AsyncApiStringReader(settings).ReadFragment<AsyncApiServer>(yaml, version, out var diagnostics);
+            diagnostics.Errors.Should().BeEmpty();
+
+            var actual = server.SerializeAsYaml(version);
+            actual.Should().Contain("qos: 1").And.NotContain("topic:").And.NotContain("retain:");
+        }
+
+        [Test]
+        public void LastWill_WithExplicitRetainFalse_WritesRetain()
+        {
+            var lastWill = new LastWill { Topic = "/last-wills", Retain = false };
+            var server = new MQTTServerBinding { LastWill = lastWill };
+
+            server.SerializeAsYaml(AsyncApiVersion.AsyncApi3_0).Should().Contain("topic: /last-wills").And.Contain("retain: false");
+        }
     }
 }