Desktop profile menu can render empty for no-OpenAI-auth providers when Settings gate is not ready/enabled

What version of the Codex App are you using (From “About Codex” dialog)?

26.601.21317

What subscription do you have?

API

What platform is your computer?

Mac

What issue are you seeing?

In Codex Desktop, the lower-left profile/settings dropdown can render as an empty menu on first open when the active provider does not require OpenAI/ChatGPT auth. This is reproducible in Meta-managed Codex, where the provider is a custom responses provider and
requiresOpenaiAuth=false. Opening Settings through another route, such as Cmd+,, appears to self-heal the dropdown.

Impact:
Users see an empty menu where they expect at least Settings. This makes Settings look broken or unavailable, especially in managed/no-auth enterprise distributions.

<img width="980" height="128" alt="Image" src="https://github.com/user-attachments/assets/fcddc8d2-ab3c-4ab8-bf07-65fbc84767a3" />

What steps can reproduce the bug?

1. Launch Codex Desktop in a no-OpenAI-auth configuration.
2. Before opening Settings anywhere else, click the lower-left profile/settings menu.
3. The menu opens but contains zero visible actions.
4. Open Settings via native menu or keyboard shortcut.
5. Reopen the lower-left menu.
6. The menu now shows Settings.

What is the expected behavior?

The profile/settings dropdown should always include Settings in desktop builds, regardless of account state, auth method, or Statsig readiness.

Additional information

Likely cause:
The profile dropdown has no account rows in requiresOpenaiAuth=false mode, which is valid. The fallback Settings row appears to be gated behind Statsig gate 4166894088. If that gate is false or not initialized on first open, the dropdown has no rows to render.

Evidence:
Installed desktop bundle shows the Settings item rendered as Pt && <Settings row>, where Pt = se("4166894088"). In no-auth provider mode, ChatGPT/Profile/Usage/Logout rows are absent by design, so this gate controls whether the menu has any useful item at all.