fix: unify PiP window creation through single frontend code path

Rust global shortcuts (Ctrl+1-5) now emit a pip:open event instead of
creating windows directly, so geometry restore, loading spinner and
state tracking all work regardless of how the PiP is opened.

src-tauri/src/lib.rs

@@ -1,7 +1,7 @@
 use tauri::{
     menu::{Menu, MenuItem},
     tray::{MouseButton, MouseButtonState, TrayIconBuilder, TrayIconEvent},
-    Manager, WebviewWindowBuilder, WindowEvent,
+    Emitter, Manager, WindowEvent,
 };
 use tauri_plugin_global_shortcut::{Code, GlobalShortcutExt, Modifiers, Shortcut, ShortcutState};
 
@@ -22,23 +22,8 @@ fn open_pip_terminal(app: &tauri::AppHandle, idx: u8) {
         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();
+    // Delegate creation to frontend (handles geometry restore, loading spinner, state tracking)
+    let _ = app.emit("pip:open", idx);
 }
 
 #[cfg_attr(mobile, tauri::mobile_entry_point)]