Add client completion notification and details (#1368)

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

src/ModelContextProtocol.Core/McpSessionHandler.cs

@@ -153,6 +153,15 @@ internal sealed partial class McpSessionHandler : IAsyncDisposable
     /// </summary>
     public string? NegotiatedProtocolVersion { get; set; }
 
+    /// <summary>
+    /// Gets a task that completes when the client session has completed, providing details about the closure.
+    /// Completion details are resolved from the transport's channel completion exception: if a transport
+    /// completes its channel with a <see cref="TransportClosedException"/>, the wrapped
+    /// <see cref="ClientCompletionDetails"/> is unwrapped. Otherwise, a default instance is returned.
+    /// </summary>
+    internal Task<ClientCompletionDetails> CompletionTask => 
+        field ??= GetCompletionDetailsAsync(_transport.MessageReader.Completion);
+
     /// <summary>
     /// Starts processing messages from the transport. This method will block until the transport is disconnected.
     /// This is generally started in a background task or thread from the initialization logic of the derived class.
@@ -305,6 +314,28 @@ internal sealed partial class McpSessionHandler : IAsyncDisposable
         }
     }
 
+    /// <summary>
+    /// Resolves <see cref="ClientCompletionDetails"/> from the transport's channel completion.
+    /// If the channel was completed with a <see cref="TransportClosedException"/>, the wrapped
+    /// details are returned. Otherwise a default instance is created from the completion state.
+    /// </summary>
+    private static async Task<ClientCompletionDetails> GetCompletionDetailsAsync(Task channelCompletion)
+    {
+        try
+        {
+            await channelCompletion.ConfigureAwait(false);
+            return new ClientCompletionDetails();
+        }
+        catch (TransportClosedException tce)
+        {
+            return tce.Details;
+        }
+        catch (Exception ex)
+        {
+            return new ClientCompletionDetails { Exception = ex };
+        }
+    }
+
     private async Task HandleMessageAsync(JsonRpcMessage message, CancellationToken cancellationToken)
     {
         Histogram<double> durationMetric = _isServer ? s_serverOperationDuration : s_clientOperationDuration;
@@ -885,9 +916,11 @@ internal sealed partial class McpSessionHandler : IAsyncDisposable
             {
                 await _messageProcessingTask.ConfigureAwait(false);
             }
-            catch (OperationCanceledException)
+            catch
             {
-                // Ignore cancellation
+                // Ignore exceptions from the message processing loop. It may fault with
+                // OperationCanceledException on normal shutdown or TransportClosedException
+                // when the transport's channel completes with an error.
             }
         }