Fix SendRequestAsync hang on Streamable HTTP SSE retry

src/ModelContextProtocol.Core/McpSessionHandler.cs

@@ -536,7 +536,38 @@ public async Task<JsonRpcResponse> SendRequestAsync(JsonRpcRequest request, Canc
                 LogSendingRequest(EndpointName, request.Method);
             }
 
-            await SendToRelatedTransportAsync(request, cancellationToken).ConfigureAwait(false);
+            // For most requests, wait for either the transport send to complete or for the
+            // response to arrive via a concurrent channel (e.g. the background GET SSE stream
+            // in Streamable HTTP). Without this, the foreground transport send could block
+            // indefinitely waiting for a response that was already delivered via a different stream.
+            //
+            // For the initialize request, always await the send to completion. The transport's
+            // SendMessageAsync has side effects (setting SessionId, starting background tasks)
+            // that must complete before subsequent messages are sent.
+            if (!tcs.Task.IsCompleted)
+            {
+                Task sendTask = SendToRelatedTransportAsync(request, cancellationToken);
+                if (method == RequestMethods.Initialize ||
+                    sendTask == await Task.WhenAny(sendTask, tcs.Task).ConfigureAwait(false))
+                {
+                    await sendTask.ConfigureAwait(false);
+                }
+                else
+                {
+                    // The response arrived via a concurrent channel before the transport send completed.
+                    // Let the send finish naturally but observe any faults at debug level.
+                    _ = sendTask.ContinueWith(
+                        static (t, s) =>
+                        {
+                            var handler = (McpSessionHandler)s!;
+                            handler.LogTransportSendFaulted(handler.EndpointName, t.Exception!);
+                        },
+                        this,
+                        CancellationToken.None,
+                        TaskContinuationOptions.OnlyOnFaulted,
+                        TaskScheduler.Default);
+                }
+            }
 
             // Now that the request has been sent, register for cancellation. If we registered before,
             // a cancellation request could arrive before the server knew about that request ID, in which
@@ -1078,4 +1109,7 @@ private static McpProtocolException CreateRemoteProtocolException(JsonRpcError e
 
     [LoggerMessage(Level = LogLevel.Trace, Message = "{EndpointName} session {SessionId} disposed with transport {TransportKind}")]
     private partial void LogSessionDisposed(string endpointName, string sessionId, string transportKind);
+
+    [LoggerMessage(Level = LogLevel.Debug, Message = "{EndpointName} transport send faulted after response was already received.")]
+    private partial void LogTransportSendFaulted(string endpointName, Exception exception);
 }