Delete conversations from the left sidebar

What variant of Codex are you using?

Codex CLI (v0.132.0)

What feature would you like to see?

Problem
The left sidebar lists all past conversations in a flat list, but there is no way to delete or remove old/unwanted conversations from the UI. Over time the list accumulates stale sessions (e.g., quick tests, experiments, abandoned tasks), making it harder to find relevant conversations.

Proposed solution
Add a way to delete a conversation from the left sidebar. Options:

Hover delete button: When hovering over a conversation entry in the sidebar, show a small trash/delete icon (🗑️) on the right edge. Clicking it removes the conversation.
Right-click context menu: Right-clicking a conversation entry shows a menu with "Delete" option.
Keyboard shortcut: With a conversation selected in the sidebar, pressing Delete or Backspace removes it, with a confirmation prompt.
Deleting should:

Remove the entry from session_index.jsonl
Move or delete the corresponding .jsonl file from sessions/YYYY/MM/DD/
Why this matters

Keeps the conversation list clean and organized
Reduces clutter when iterating on many small tasks
Provides a basic data management capability expected in any conversation-based UI
Alternatives considered

Archiving (to archived_sessions/) instead of permanent deletion — could be offered as a secondary option
Bulk select + delete for power users
Additional context
Session data is stored at ~/.codex/session_index.jsonl and ~/.codex/sessions/YYYY/MM/DD/*.jsonl. Currently users must manually edit these files from the terminal to remove conversations.

Additional information

_No response_