Fix race condition: pending request registered after reading loop cleanup

When a child process exits immediately, the message reading loop can detect
EOF and complete its cleanup sweep of _pendingRequests before SendRequestAsync
registers the initialize request's TaskCompletionSource. The TCS is then never
signaled, causing McpClient.CreateAsync to hang indefinitely.

Fix: Set a _messageProcessingComplete flag before the sweep, and check it in
SendRequestAsync after registering the TCS. This ensures that either the sweep
finds the TCS, or SendRequestAsync detects the flag and fails the TCS itself.

This race was the root cause of intermittent test host hangs on .NET 9+ in CI,
where short-lived child processes (echo to stderr, exit 1) would exit before
the session initialization request was sent.

Diagnostic evidence:
- xUnit diagnostic log shows the test's async Task starts but never completes
- dumpasync shows zero MCP state machines on the heap (entire chain GC'd)
- Hang only on .NET 9+ (different timing vs .NET 8 avoids the race)
- Always one of the StdioClientTransport stderr callback tests

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

Author: ericstj

src/ModelContextProtocol.Core/McpSessionHandler.cs

@@ -91,6 +91,7 @@ internal static bool SupportsPrimingEvent(string? protocolVersion)
 
     private CancellationTokenSource? _messageProcessingCts;
     private Task? _messageProcessingTask;
+    private volatile bool _messageProcessingComplete;
 
     /// <summary>
     /// Initializes a new instance of the <see cref="McpSessionHandler"/> class.
@@ -325,6 +326,9 @@ ex is OperationCanceledException &&
             }
 
             // Fail any pending requests, as they'll never be satisfied.
+            // Set the flag before sweeping so that any request registered concurrently
+            // via SendRequestAsync after the sweep will see it and fail itself.
+            _messageProcessingComplete = true;
             foreach (var entry in _pendingRequests)
             {
                 entry.Value.TrySetException(new IOException("The server shut down unexpectedly."));
@@ -569,6 +573,18 @@ public async Task<JsonRpcResponse> SendRequestAsync(JsonRpcRequest request, Canc
 
         var tcs = new TaskCompletionSource<JsonRpcMessage>(TaskCreationOptions.RunContinuationsAsynchronously);
         _pendingRequests[request.Id] = tcs;
+
+        // If message processing has already completed (transport closed), fail the request
+        // immediately. This handles the race where the reading loop's cleanup sweep ran
+        // before this request was registered, so it was missed by the sweep.
+        if (_messageProcessingComplete)
+        {
+            if (_pendingRequests.TryRemove(request.Id, out var removed))
+            {
+                removed.TrySetException(new IOException("The server shut down unexpectedly."));
+            }
+        }
+
         try
         {
             if (addTags)