Desktop task menu: add permanent deletion for accidental branch conversations

Problem

In the Windows Codex Desktop app, an accidental “Branch to new chat” creates a separate, unwanted task/conversation. Its overflow menu exposes Archive, but not Delete.

For a user who opened a branch by mistake and no longer needs it, archive is not an equivalent to permanent deletion: the unwanted branch still exists in archived history and there is no clear way to remove it.

Reproduction

1. Open a Codex Desktop conversation.
2. Accidentally choose Branch to new chat.
3. Open the overflow menu for the newly created branch task.
4. Observe options such as Pin, Rename, Mark as unread, Archive, Project, Section, Share, Copy, and Open in new window.
5. There is no Delete action.

Current behavior

• The accidental branch can be archived but not permanently deleted from the task menu.
• The user cannot distinguish whether archive only hides the task, retains all history indefinitely, or affects project workspace files.
• This is especially confusing in project-based workflows where accidental branches create sidebar clutter.

Expected behavior

Provide an explicit Delete task/conversation action for an accidental branch, ideally available after navigating back to the parent task.

The confirmation dialog should state clearly:

• this deletes only the selected conversation/task history;
• it does not delete the parent conversation;
• it does not delete project workspace files;
• deletion is irreversible.

Why this matters

Branching is useful, but accidental branching is easy. Users need a clear lifecycle distinction:

• Archive: hide/recover later;
• Delete: permanently remove an unwanted branch;
• Parent task: unaffected.

This would reduce task-list clutter and prevent users from being forced to keep mistaken branch conversations indefinitely.

Environment

• Codex Desktop on Windows
• Exact application version was not captured
• No project files or user data need to be included to reproduce this UI issue

User impact

A user explicitly wanted to delete a mistakenly created branch and could only see Archive in the UI. The lack of Delete caused repeated confusion about whether the branch could be removed and whether archiving would affect the parent project.

No files, tests, or entry points are named. Start by locating the Desktop task overflow menu and the existing Branch and Archive handling, then trace how task history and parent relationships are represented. Done means an explicit Delete action with confirmation that only removes the selected conversation, leaves the parent and workspace files untouched, and states that deletion is irreversible.