codex - 💡(How to fix) Fix Add Temporary Chat mode for sensitive Codex desktop sessions

Codex desktop should support a Temporary Chat mode for sensitive one-off coding sessions.

Comparable products already expose this pattern:

• ChatGPT web calls it Temporary Chat.
• Claude Desktop exposes an Incognito chat ghost icon in its Chat surface.

Codex desktop is different from Claude Desktop: Claude has separate Chat, Cowork, and Code surfaces, while Codex desktop is primarily the coding/session interface. That means the equivalent feature should apply directly when starting a new Codex session, not only to a separate general-chat tab.

Expected behavior:

• A visible Temporary Chat or ghost/private-mode control when starting a new Codex desktop session.
• The session does not appear in normal sidebar/history after close.
• Resume is disabled.
• Local transcript/session/log persistence is disabled or clearly minimized.
• Connected apps/tools are disabled by default unless explicitly enabled for that temporary session.
• Workspace/file access starts from the narrowest possible scope.
• The UI includes a clear retention notice for any server-side safety/security retention.
• The mode is available for projectless/scratch sessions at minimum, even if full repo-attached sessions need extra constraints.

Why this matters:

Codex sessions often have access to local files, repos, tool output, and connected app context. Users need a lightweight way to ask sensitive one-off questions or do narrow coding work without creating a durable session artifact or pulling in broader workspace context.

Related prior issue: https://github.com/openai/codex/issues/6527 requested CLI incognito mode and was closed as not planned. This request is specifically for Codex desktop UX and Temporary Chat parity with ChatGPT and Claude Desktop.