feat(tui) render request_permissions calls (#14004)

## Summary
Adds support for tui rendering of request_permission calls

<img width="724" height="245" alt="Screenshot 2026-03-08 at 9 04 07 PM"
src="https://github.com/user-attachments/assets/e1997825-a496-4bfb-bbda-43d0006460a5"
/>


## Testing
- [x] Added snapshot test

codex-rs/tui/src/app.rs

@@ -1171,6 +1171,15 @@ impl App {
                     ))
                 }
             }
+            EventMsg::RequestPermissions(ev) => Some(ThreadInteractiveRequest::Approval(
+                ApprovalRequest::Permissions {
+                    thread_id,
+                    thread_label,
+                    call_id: ev.call_id.clone(),
+                    reason: ev.reason.clone(),
+                    permissions: ev.permissions.clone(),
+                },
+            )),
             _ => None,
         }
     }
@@ -3237,6 +3246,30 @@ impl App {
                         "E X E C".to_string(),
                     ));
                 }
+                ApprovalRequest::Permissions {
+                    permissions,
+                    reason,
+                    ..
+                } => {
+                    let _ = tui.enter_alt_screen();
+                    let mut lines = Vec::new();
+                    if let Some(reason) = reason {
+                        lines.push(Line::from(vec!["Reason: ".into(), reason.italic()]));
+                        lines.push(Line::from(""));
+                    }
+                    if let Some(rule_line) =
+                        crate::bottom_pane::format_additional_permissions_rule(&permissions)
+                    {
+                        lines.push(Line::from(vec![
+                            "Permission rule: ".into(),
+                            rule_line.cyan(),
+                        ]));
+                    }
+                    self.overlay = Some(Overlay::new_static_with_renderables(
+                        vec![Box::new(Paragraph::new(lines).wrap(Wrap { trim: false }))],
+                        "P E R M I S S I O N S".to_string(),
+                    ));
+                }
                 ApprovalRequest::McpElicitation {
                     server_name,
                     message,