Make ClientTransportClosedException public and unify transport exception handling (#1467)

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: stephentoub <2642209+stephentoub@users.noreply.github.com>
Co-authored-by: halter73 <54385+halter73@users.noreply.github.com>
Co-authored-by: Stephen Toub <stoub@microsoft.com>

src/ModelContextProtocol.Core/Server/StreamServerTransport.cs

@@ -80,6 +80,10 @@ public class StreamServerTransport : TransportBase
             await _outputStream.WriteAsync(s_newlineBytes, cancellationToken).ConfigureAwait(false);
             await _outputStream.FlushAsync(cancellationToken).ConfigureAwait(false);
         }
+        catch (OperationCanceledException) when (cancellationToken.IsCancellationRequested)
+        {
+            throw;
+        }
         catch (Exception ex)
         {
             LogTransportSendFailed(Name, id, ex);