Add explicit deletion controls for archived Codex cloud sessions

Problem

Codex cloud sessions appear to remain available as archived conversations long after they were used. This is a serious privacy and data-retention concern for a developer tool.

Archiving is not deletion. For coding workflows, archived sessions may contain sensitive project context, repository names, file paths, logs, diffs, prompts, implementation details, and occasionally accidental secrets. Hiding these sessions from the main UI does not satisfy the expected behavior of deleting developer work sessions.

I previously reported a related issue for local Codex state stored under ./codex, where chat/session data was not clearly removable. The same problem now appears to exist for Codex cloud sessions: there is no obvious, dedicated, auditable way to delete old Codex cloud task history separately from normal ChatGPT conversations.

Expected behavior

Codex should provide explicit deletion controls for cloud sessions:

• Delete a single Codex cloud session permanently.
• Delete all archived Codex cloud sessions.
• Delete all Codex cloud task history independently from normal ChatGPT chats.
• Clearly distinguish Archive from Delete in the Codex UI.
• Show retention status after deletion, for example "scheduled for deletion".
• Provide an option to disable persistent Codex cloud session history by default.
• Provide a temporary/private Codex task mode where sessions are not retained beyond the minimum operational window.

Actual behavior

Old Codex cloud sessions are still visible as archived conversations. The current behavior makes it easy to assume that old sessions were removed or are no longer retained, when in practice they appear to remain associated with the account.

For developer tooling, this is a higher-risk default than normal chat history because Codex sessions can contain project-specific and security-sensitive information.

Why this matters

A coding assistant should treat cloud task history as sensitive developer data, not as ordinary chat clutter.

Archive is useful for organization, but it is not a privacy control. Users need a clear deletion path and a way to verify that old Codex cloud sessions are no longer retained in their account.

This is especially important because Codex can interact with private repositories, local development context, logs, stack traces, dependency information, and internal implementation details.

Requested fix

Please add dedicated Codex data controls for cloud sessions:

1. A Codex-specific history/data section.
2. Bulk deletion for archived Codex cloud sessions.
3. Per-session deletion from the Codex cloud/task UI.
4. A retention setting for Codex cloud tasks.
5. Clear UI language that "Archive" means "hide", not "delete".
6. Documentation explaining where Codex cloud sessions are stored, how long they are retained, and how users can permanently delete them.

Security/privacy impact

This is not only a UX issue. It affects user trust and data minimization for developer workflows. A user should not have to search through archived general chats to discover old Codex cloud sessions from months ago.

Codex should make deletion explicit, separate, and easy to audit.