Codex / ChatGPT sign-in is missing from Agents Window after enabling documented settings

### VS Code Version
1.138.0 Stable

### OS
Windows x64

### Problem

I followed the official documentation for using Codex in the Agents Window without GitHub sign-in:

https://code.visualstudio.com/docs/agents/run/agent-harnesses#_use-codex-without-github-sign-in-experimental

I enabled:

`chat.agentHost.codexAgent.enabled`
`chat.agentHost.allowSignedOutWhenUsable`
`chat.editor.codex.preferAgentHost`

Then I reloaded/restarted VS Code.

However, in the dedicated Agents Window:

- There is no `Sign in to ChatGPT` option.
- The Session Target / Agent picker only shows Copilot and Claude.
- Codex does not appear at all.
- Therefore I cannot use my ChatGPT subscription to run Codex as an Agent Host harness.

### Steps to reproduce

1. Install VS Code 1.138.0 Stable.
2. Enable `chat.agentHost.codexAgent.enabled`.
3. Enable `chat.agentHost.allowSignedOutWhenUsable`.
4. Reload VS Code.
5. Run `Chat: Open Agents Window`.
6. Open the account menu or create a new Agent session.

### Actual behavior

Only GitHub/Copilot sign-in is available. Codex is missing from the Agents Window and there is no ChatGPT login entry.

### Expected behavior

According to the documentation, after enabling Agent Host Codex, the Agents Window should allow `Sign in to ChatGPT` and selecting Codex as the Agent/Harness using a ChatGPT subscription without requiring GitHub Copilot.

### Additional note

This report is specifically about the dedicated Agents Window / Agent Host Codex integration, not the OpenAI Codex VS Code extension or the normal Chat sidebar.