[Browser Rendering] Playwright mcp example code needs update (#25416)

Author: ToriLindsay

src/content/docs/browser-rendering/platform/playwright-mcp.mdx

@@ -79,7 +79,22 @@ import { env } from 'cloudflare:workers';
 import { createMcpAgent } from '@cloudflare/playwright-mcp';
 
 export const PlaywrightMCP = createMcpAgent(env.BROWSER);
-export default PlaywrightMCP.mount('/sse');
+
+export default {
+  fetch(request: Request, env: Env, ctx: ExecutionContext) {
+    const { pathname } = new URL(request.url);
+
+    switch (pathname) {
+      case '/sse':
+      case '/sse/message':
+        return PlaywrightMCP.serveSSE('/sse').fetch(request, env, ctx);
+      case '/mcp':
+        return PlaywrightMCP.serve('/mcp').fetch(request, env, ctx);
+      default:
+        return new Response('Not Found', { status: 404 });
+    }
+  },
+};
 ```
 
 4. Deploy the server.