Fix SendRequestAsync hang when background SSE stream delivers response before foreground transport send completes

Replace `await SendToRelatedTransportAsync(request, cancellationToken)` with
`Task.WhenAny(sendTask, tcs.Task)` so that if the response TCS completes
first (via a concurrent background channel such as the background GET SSE
stream in Streamable HTTP), execution proceeds immediately without waiting
for the foreground send. If the send completes first (normal case), it is
awaited directly, preserving the original behavior. The still-running send
task's exceptions are observed via a fire-and-forget ContinueWith(OnlyOnFaulted)
to prevent unobserved task exceptions.

Co-authored-by: stephentoub <2642209+stephentoub@users.noreply.github.com>

Author: Copilot

src/ModelContextProtocol.Core/McpSessionHandler.cs

@@ -536,7 +536,26 @@ public async Task<JsonRpcResponse> SendRequestAsync(JsonRpcRequest request, Canc
                 LogSendingRequest(EndpointName, request.Method);
             }
 
-            await SendToRelatedTransportAsync(request, cancellationToken).ConfigureAwait(false);
+            // 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.
+            Task sendTask = SendToRelatedTransportAsync(request, cancellationToken);
+            if (sendTask != await Task.WhenAny(sendTask, tcs.Task).ConfigureAwait(false))
+            {
+                // The response arrived via a concurrent channel before the transport send completed.
+                // Observe any exception from the still-running send to prevent unobserved task exceptions.
+                _ = sendTask.ContinueWith(
+                    static (t, _) => _ = t.Exception,
+                    null,
+                    CancellationToken.None,
+                    TaskContinuationOptions.OnlyOnFaulted,
+                    TaskScheduler.Default);
+            }
+            else
+            {
+                await sendTask.ConfigureAwait(false);
+            }
 
             // 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