feat(cli): add browse-cli metadata to Browserbase sessions (#1890)

## Summary
- Adds `userMetadata: { "browse-cli": "true" }` to every Browserbase
session created through the browse CLI
- Enables usage attribution to distinguish CLI-originated sessions from
SDK-originated ones

## Test plan
- [x] Run `browse open https://example.com` in Browserbase mode and
verify the session has `browse-cli: true` in its metadata
- [x] Verify local mode is unaffected

🤖 Generated with [Claude Code](https://claude.com/claude-code)

<!-- This is an auto-generated description by cubic. -->
---
## Summary by cubic
Adds `userMetadata: { "browse-cli": "true" }` to
`browserbaseSessionCreateParams` for sessions started by
`@browserbasehq/browse-cli` in Browserbase mode, enabling usage
attribution and distinguishing CLI vs SDK sessions. Satisfies STG-1678;
local mode is unaffected.

<sup>Written for commit 58c10fd.
Summary will update on new commits. <a
href="https://cubic.dev/pr/browserbase/stagehand/pull/1890">Review in
cubic</a></sup>

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

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: shrey150

.changeset/browse-cli-metadata.md

@@ -0,0 +1,5 @@
+---
+"@browserbasehq/browse-cli": patch
+---
+
+Add browse-cli metadata to Browserbase sessions created through the CLI

packages/cli/src/index.ts

@@ -346,15 +346,16 @@ async function runDaemon(session: string, headless: boolean): Promise<void> {
         ...(useBrowserbase
           ? {
               disableAPI: true,
-              ...(contextConfig
-                ? {
-                    browserbaseSessionCreateParams: {
+              browserbaseSessionCreateParams: {
+                userMetadata: { "browse-cli": "true" },
+                ...(contextConfig
+                  ? {
                       browserSettings: {
                         context: contextConfig,
                       },
-                    },
-                  }
-                : {}),
+                    }
+                  : {}),
+              },
             }
           : {
               localBrowserLaunchOptions: {