feat: compact boundary divider, overlay fix, approval window, PiP, Tauri enhancements

- Add CompactBoundaryDivider component for compact_boundary system messages
- Fix readability overlay: v-if removes element entirely at 0% opacity
- Add approval page and window composable
- Add PiP window support and loading screen
- Tauri: add window management commands and capabilities
- Disable Ctrl+1..5 shortcuts in Tauri (handled by global shortcuts)

src-tauri/src/lib.rs

@@ -1,3 +1,46 @@
+use tauri::{
+    menu::{Menu, MenuItem},
+    tray::{MouseButton, MouseButtonState, TrayIconBuilder, TrayIconEvent},
+    Manager, WebviewWindowBuilder, WindowEvent,
+};
+use tauri_plugin_global_shortcut::{Code, GlobalShortcutExt, Modifiers, Shortcut, ShortcutState};
+
+fn show_main_window(app: &tauri::AppHandle) {
+    if let Some(window) = app.get_webview_window("main") {
+        let _ = window.show();
+        let _ = window.unminimize();
+        let _ = window.set_focus();
+    }
+}
+
+fn open_pip_terminal(app: &tauri::AppHandle, idx: u8) {
+    let label = format!("pip-terminal-{}", idx);
+
+    // If PiP already exists, just focus it
+    if let Some(win) = app.get_webview_window(&label) {
+        let _ = win.set_focus();
+        return;
+    }
+
+    // Create new PiP window — the page itself handles terminal connection or showing "new session" modal
+    let url = format!("/transcript-debug/{}?pip=1", idx);
+    let x = 1520.0_f64; // sensible default, will be near right edge on 1920px screens
+    let y = 60.0 + (idx as f64 - 1.0) * 40.0;
+
+    let _ = WebviewWindowBuilder::new(
+        app,
+        &label,
+        tauri::WebviewUrl::App(url.into()),
+    )
+    .title(&format!("T{} - Agent UI", idx))
+    .inner_size(380.0, 620.0)
+    .position(x, y)
+    .decorations(false)
+    .resizable(true)
+    .focused(true)
+    .build();
+}
+
 #[cfg_attr(mobile, tauri::mobile_entry_point)]
 pub fn run() {
     tauri::Builder::default()
@@ -6,6 +49,96 @@ pub fn run() {
         .plugin(tauri_plugin_notification::init())
         .plugin(tauri_plugin_clipboard_manager::init())
         .plugin(tauri_plugin_dialog::init())
+        .plugin(
+            tauri_plugin_global_shortcut::Builder::new()
+                .with_handler(|app, shortcut, event| {
+                    if event.state != ShortcutState::Pressed {
+                        return;
+                    }
+
+                    let mods = shortcut.mods;
+                    let key = shortcut.key;
+
+                    // Ctrl+Alt+E → show main window
+                    if mods == Modifiers::CONTROL | Modifiers::ALT && key == Code::KeyE {
+                        show_main_window(app);
+                        return;
+                    }
+
+                    // Ctrl+1-5 → open PiP terminal
+                    if mods == Modifiers::CONTROL {
+                        match key {
+                            Code::Digit1 => open_pip_terminal(app, 1),
+                            Code::Digit2 => open_pip_terminal(app, 2),
+                            Code::Digit3 => open_pip_terminal(app, 3),
+                            Code::Digit4 => open_pip_terminal(app, 4),
+                            Code::Digit5 => open_pip_terminal(app, 5),
+                            _ => {}
+                        }
+                    }
+                })
+                .build(),
+        )
+        .setup(|app| {
+            // Register global shortcuts (desktop only)
+            #[cfg(desktop)]
+            {
+                let ctrl_alt = Modifiers::CONTROL | Modifiers::ALT;
+                let ctrl = Modifiers::CONTROL;
+                let shortcuts = [
+                    Shortcut::new(Some(ctrl_alt), Code::KeyE),
+                    Shortcut::new(Some(ctrl), Code::Digit1),
+                    Shortcut::new(Some(ctrl), Code::Digit2),
+                    Shortcut::new(Some(ctrl), Code::Digit3),
+                    Shortcut::new(Some(ctrl), Code::Digit4),
+                    Shortcut::new(Some(ctrl), Code::Digit5),
+                ];
+                for s in &shortcuts {
+                    let _ = app.global_shortcut().register(*s);
+                }
+            }
+
+            // Build system tray (desktop only)
+            #[cfg(desktop)]
+            {
+                let show_item = MenuItem::with_id(app, "show", "Show", true, None::<&str>)?;
+                let quit_item = MenuItem::with_id(app, "quit", "Quit", true, None::<&str>)?;
+                let menu = Menu::with_items(app, &[&show_item, &quit_item])?;
+
+                TrayIconBuilder::new()
+                    .icon(app.default_window_icon().unwrap().clone())
+                    .menu(&menu)
+                    .show_menu_on_left_click(false)
+                    .on_menu_event(|app, event| match event.id.as_ref() {
+                        "show" => show_main_window(app),
+                        "quit" => app.exit(0),
+                        _ => {}
+                    })
+                    .on_tray_icon_event(|tray, event| {
+                        if let TrayIconEvent::Click {
+                            button: MouseButton::Left,
+                            button_state: MouseButtonState::Up,
+                            ..
+                        } = event
+                        {
+                            show_main_window(tray.app_handle());
+                        }
+                    })
+                    .build(app)?;
+            }
+
+            Ok(())
+        })
+        .on_window_event(|window, event| {
+            // Hide main window to tray instead of closing (desktop only)
+            #[cfg(desktop)]
+            if let WindowEvent::CloseRequested { api, .. } = event {
+                if window.label() == "main" {
+                    api.prevent_close();
+                    let _ = window.hide();
+                }
+            }
+        })
         .run(tauri::generate_context!())
         .expect("error while running tauri application");
 }