[App] Allow agent thread search to include archived tasks

What variant of Codex are you using?

App — ChatGPT desktop for macOS

What feature would you like to see?

Expose archived tasks through the agent-facing thread search control. The current codex_app__list_threads tool accepts query and limit, but it has no archive-state filter and excludes archived tasks from results.

Please add an option such as:

archiveState: active | archived | all

or an includeArchived boolean. Search results should also expose archived and archivedAt metadata.

This would allow a manager task to locate and reuse completed work without requiring the user to manually unarchive tasks or requiring the agent to inspect internal local state. Ideally, the same behavior would work consistently for local and connected-host tasks.

Additional information

Verified behavior on ChatGPT desktop build 26.707.71524 (5263), macOS 26.5.2, Apple Silicon:

1. Choose an existing archived task with a known unique title.
2. Call codex_app__list_threads using that title as the query.
3. The result is empty.
4. Call codex_app__read_thread with the already-known archived task ID.
5. The archived task and its history are returned successfully.

This shows that archived tasks remain readable, but they are not discoverable through the agent thread-search control.

Related: #20732 requests archived-task visibility in the normal desktop UI. This request is specifically for the agent-facing thread-management tool/API.

Expected outcome: agent tasks can search active, archived, or all tasks explicitly, without changing archive state. No task IDs, project names, or archived conversation content are included in this report.