[Windows][Browser] Browser control fails with API-key authentication

Summary

On Windows, browser control through the Edge plugin is unavailable when Codex is authenticated with an OpenAI API key. The browser extension and native host connect successfully, but the first browser operation fails with unsupported Codex auth method: apikey.

This issue is intended to clarify whether browser control requires ChatGPT OAuth authentication and whether API-key-authenticated users are expected to be unsupported.

Environment

• Windows
• Codex Desktop: 26.901.6511.0
• Microsoft Edge stable
• OpenAI browser extension: 1.26.901.11451_0
• Codex authentication: API key (auth_mode=apikey)

Steps to reproduce

1. Configure Codex Desktop/CLI with API-key authentication.
2. Install and enable the OpenAI browser extension in Microsoft Edge.
3. Start browser control and list the user's open tabs.

Actual behavior

The extension/native-host diagnostics pass, but the browser operation fails:

edge.user.openTabs()
unsupported Codex auth method: apikey

Verified locally:

• Edge is running.
• The extension is installed and enabled.
• The native messaging host manifest is present and valid for Edge.
• The browser runtime can select the Edge extension browser.

No token values or private credentials are included.

Expected behavior

• If API-key authentication is not supported for browser control, show a clear user-facing message and document the requirement for ChatGPT OAuth login.
• If API-key authentication is supported, browser read/control operations should work without this error.

Reference: https://learn.chatgpt.com/zh-Hans/docs/auth?surface=app

Reproduce the failure on Windows with Codex API-key authentication, the Edge extension, and browser control's open-tabs operation. Trace the authentication check that emits "unsupported Codex auth method: apikey" and confirm whether API-key access is supported; done means browser operations work or the user-facing message and OAuth requirement are clearly documented.