Improve exception diagnostics for stdio client (#376)

* Improve exception diagnostics for stdio client

Track the last several lines of stderr and include those in an exception created as part of CleanupAsync if the server process has already exited. This is based on an assumption that the server should never exit prior to CleanupAsync being called.

* Address feedback and fix test failure

src/ModelContextProtocol/Shared/McpSession.cs

@@ -197,7 +197,7 @@ internal sealed partial class McpSession : IDisposable
             // Fail any pending requests, as they'll never be satisfied.
             foreach (var entry in _pendingRequests)
             {
-                entry.Value.TrySetException(new InvalidOperationException("The server shut down unexpectedly."));
+                entry.Value.TrySetException(new IOException("The server shut down unexpectedly."));
             }
         }
     }