Feature request: add a one-way privacy setting to hide ChatGPT conversations from Codex

Feature request

With the recent integration/merge between ChatGPT Work and Codex, I can now see ChatGPT conversations inside Codex. I would like to request a privacy setting that allows users to turn this behavior off from the web app.

Desired behavior

Please add a web-side setting such as:

Do not show my web/mobile ChatGPT conversations in Codex or ChatGPT Desktop.

This should work as a one-way privacy control:

• Conversations created on the web app or mobile app should be hidden from Codex / ChatGPT Desktop when the setting is enabled.
• Codex can still work normally for coding tasks.
• The setting should be controlled from the web app, so users can manage it remotely without needing access to the desktop device.

Why this matters

Some users access ChatGPT across multiple devices, including shared desktop environments. In those cases, a conversation started on the web or mobile app may become visible on a desktop Codex session, which can expose private conversations unintentionally.

A one-way visibility control would make the new ChatGPT/Codex integration safer for privacy-sensitive workflows, especially when users want to keep personal web/mobile conversations separate from coding work on a desktop machine.

Suggested implementation

A simple toggle in privacy/settings would be enough:

• Show ChatGPT conversations in Codex: on/off
• Or Sync web/mobile ChatGPT conversations to Codex: on/off

Thanks for considering this. I think this would make the merged ChatGPT + Codex experience much safer and more flexible for users who work across multiple devices.