fix: Use lowercase header names

Author: gylove1994

src/server/streamable-http.test.ts

@@ -69,7 +69,7 @@ describe("StreamableHTTPServerTransport", () => {
       expect(mockResponse.writeHead).toHaveBeenCalledWith(
         200,
         expect.objectContaining({
-          "Mcp-Session-Id": transport.sessionId,
+          "mcp-session-id": transport.sessionId,
         })
       );
     });

src/server/streamable-http.ts

@@ -113,7 +113,7 @@ export class StreamableHTTPServerTransport implements Transport {
       "Content-Type": "text/event-stream",
       "Cache-Control": "no-cache",
       Connection: "keep-alive",
-      "Mcp-Session-Id": this._sessionId,
+      "mcp-session-id": this._sessionId,
     });
 
     const connection: StreamConnection = {
@@ -214,7 +214,7 @@ export class StreamableHTTPServerTransport implements Transport {
             "Content-Type": "text/event-stream",
             "Cache-Control": "no-cache",
             Connection: "keep-alive",
-            "Mcp-Session-Id": this._sessionId,
+            "mcp-session-id": this._sessionId,
           });
 
           const connectionId = randomUUID();
@@ -249,7 +249,7 @@ export class StreamableHTTPServerTransport implements Transport {
           // use direct JSON response
           res.writeHead(200, {
             "Content-Type": "application/json",
-            "Mcp-Session-Id": this._sessionId,
+            "mcp-session-id": this._sessionId,
           });
 
           // handle each message