Windows: Chrome browser backend missing (only 'iab' available despite extension and native host working)

Summary

On Windows, Codex Desktop (Microsoft Store) cannot use the Chrome backend. The browser plugin reports only the iab backend even though the Chrome extension, Native Messaging, and extension host are all working.

Environment

• OS: Windows 11
• Codex Desktop: Microsoft Store build 26.623.9142.0
• Chrome extension: 1.1.5

Expected

Available browser backends should include the Chrome extension backend (e.g. extension), allowing Chrome control.

Actual

Prompting:
Use the browser plugin and tell me all available browser backends.
returns only:

• iab — Codex In-app Browser

The Chrome backend is absent.

Diagnostics performed

• Chrome extension installed and enabled.
• Service Worker running.
• chrome.runtime.connectNative("com.openai.codexextension") succeeds in DevTools.
• Native Messaging host registered and reachable.
• extension-host.exe is running.
• Codex Browser plugin still reports only iab.

Result

Chrome cannot be controlled from Codex even though the extension and native messaging appear healthy. This appears to be a runtime/backend registration issue rather than an installation problem.