Add user-agent (#1646)

# why
For observability into stagehand sessions

# what changed
- Added a custom `Stagehand/<version>` user agent header to CDP
connections.

# test plan


<!-- This is an auto-generated description by cubic. -->
---
## Summary by cubic
Set a custom User-Agent on CDP WebSocket connections:
Stagehand/<version> using STAGEHAND_VERSION. This helps servers identify
the client for logging and compatibility.

<sup>Written for commit 4a0c58d.
Summary will update on new commits. <a
href="https://cubic.dev/pr/browserbase/stagehand/pull/1646">Review in
cubic</a></sup>

<!-- End of auto-generated description by cubic. -->

---------

Co-authored-by: Chromie <miguel@browserbase.com>
Co-authored-by: Chromie Bot <chromie@browserbase.com>
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

Author: 4 people

.changeset/tricky-mangos-prove.md

@@ -0,0 +1,5 @@
+---
+"@browserbasehq/stagehand": patch
+---
+
+Add user-agent to CDP connections

packages/core/lib/v3/understudy/cdp.ts

@@ -1,6 +1,7 @@
 // lib/v3/understudy/cdp.ts
 import WebSocket from "ws";
 import type { Protocol } from "devtools-protocol";
+import { STAGEHAND_VERSION } from "../../version";
 
 /**
  * CDP transport & session multiplexer
@@ -97,7 +98,12 @@ export class CdpConnection implements CDPSessionLike {
   }
 
   static async connect(wsUrl: string): Promise<CdpConnection> {
-    const ws = new WebSocket(wsUrl);
+    // Include User-Agent header for server-side observability and version tracking
+    const ws = new WebSocket(wsUrl, {
+      headers: {
+        "User-Agent": `Stagehand/${STAGEHAND_VERSION}`,
+      },
+    });
     await new Promise<void>((resolve, reject) => {
       ws.once("open", () => resolve());
       ws.once("error", (e) => reject(e));