Remote Control: archived tasks on a connected host are not visible in Codex Desktop

Summary

When using Codex Remote Control with a connected host, archived tasks on that remote host are not discoverable in Codex Desktop. Active and recent remote tasks remain available, so the host connection itself is healthy.

Steps to reproduce

1. Connect Codex Desktop to a Remote Control host.
2. Create or run a task on the remote host.
3. Archive that task.
4. Return to Codex Desktop and inspect the remote host task list, archive view, and search.

Actual behavior

The archived remote task is not shown or discoverable in Codex Desktop.

Expected behavior

Archived tasks from a connected Remote Control host should remain discoverable in Codex Desktop, either in a dedicated archive view or through task search, with clear host context.

Notes

• The problem persists after reconnecting.
• Non-archived remote tasks are visible, so this does not appear to be a basic connectivity failure.
• This seems related to remote thread synchronization and archive-state handling, but is distinct from #25713, which concerns archiving the currently open local Desktop thread on Windows.
• Observed on 2026-07-14. Exact app version was not captured; I can add it if needed.