fix: extra Headers when they are a Headers object

src/client/streamableHttp.ts

@@ -174,9 +174,12 @@ export class StreamableHTTPClientTransport implements Transport {
       headers["mcp-session-id"] = this._sessionId;
     }
 
-    return new Headers(
-      { ...headers, ...this._requestInit?.headers }
-    );
+    const extraHeaders = this._normalizeHeaders(this._requestInit?.headers);
+
+    return new Headers({
+      ...headers,
+      ...extraHeaders,
+    });
   }
 
 
@@ -242,6 +245,20 @@ export class StreamableHTTPClientTransport implements Transport {
 
   }
 
+    private _normalizeHeaders(headers: HeadersInit | undefined): Record<string, string> {
+    if (!headers) return {};
+    
+    if (headers instanceof Headers) {
+      return Object.fromEntries(headers.entries());
+    }
+    
+    if (Array.isArray(headers)) {
+      return Object.fromEntries(headers);
+    }
+    
+    return { ...headers as Record<string, string> };
+  }
+
   /**
    * Schedule a reconnection attempt with exponential backoff
    *