Codex App: add manual refresh button (or auto-sync) for archived and cross-surface conversations

Summary

The macOS app has multiple refresh/sync gaps:

• cross-surface sync behaves differently between VS Code extension and CLI
• conversation list does not refresh correctly after restoring a thread from Archive inside the app

Observed behavior

| macOS app state | Where conversation is created/continued | Actual behavior |
|---|---|---|
| App is already open | Restore a conversation from Archive in macOS app | Restored conversation does not appear in the active list until app restart |
| App is already open | Create a new conversation in VS Code extension | New conversation does not appear in app |
| App is already open | Create a new conversation in CLI | New conversation does not appear in app |
| App is opened after conversation was created in VS Code extension | Continue chatting in VS Code extension | App can see the conversation and continues to receive new turns (works) |
| App is opened after conversation was created in CLI | Continue chatting in CLI | App can see the conversation entry, but new CLI turns do not refresh in app |

Expected behavior

• Restoring a conversation from Archive should immediately update the active conversation list in the macOS app.
• The macOS app should discover newly created conversations from both VS Code extension and CLI while the app is open.
• After opening the app, new turns from both VS Code extension and CLI should keep syncing consistently.
• A visible Refresh button in the app would be a useful fallback when real-time sync misses updates.

Repro steps

Case A: restore from Archive inside app

1. Open the macOS app.
2. Go to Archive and move one archived conversation back to active.
3. Return to the active conversation list.
4. The restored conversation does not appear until app restart.

Case B: app already open (new conversation from CLI/VS Code)

1. Open the macOS app.
2. Create a new conversation in CLI (or VS Code extension).
3. Check the app conversation list.
4. New conversation is not shown.

Case C: app opened later (VS Code path)

1. Create a new conversation in VS Code extension.
2. Open the macOS app.
3. Continue chatting in VS Code extension.
4. App receives new turns (works).

Case D: app opened later (CLI path)

1. Create a new conversation in CLI.
2. Open the macOS app.
3. Continue chatting in CLI.
4. App does not refresh newly added CLI turns.

Environment

• Codex App version: 26.212.1823 (build 661)
• macOS: 26.3 (build 25D125)

Related issues

• #5609
• #2153