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.

frontend/src/App.vue

@@ -25,6 +25,7 @@ import { isTauri, isMobileTauri, getTauriNotification } from './lib/tauri'
 import { initApprovalNotifications } from './services/approvalNotifications'
 import { useServerConfig } from './stores/server-config'
 import { useApprovalWindow } from './composables/useApprovalWindow'
+import { usePipWindow } from './composables/usePipWindow'
 
 const route = useRoute()
 const router = useRouter()
@@ -35,6 +36,7 @@ const showServerConfig = ref(false)
 const needsServerConfig = computed(() => isTauri && serverConfig && !serverConfig.isConfigured)
 
 const isPipWindow = computed(() => route.query.pip === '1' || route.query.window === '1')
+let unlistenPipOpen: (() => void) | null = null
 const showVoice = ref(false)
 const showTranscriptDebug = ref(false)
 const showDebugConsole = ref(false)
@@ -271,8 +273,15 @@ onMounted(async () => {
   fetchApprovalPending()
 
   // Initialize native approval notifications (Tauri only)
+  // Listen for PiP open requests from Rust global shortcuts (Ctrl+1-5)
   if (isTauri) {
     initApprovalNotifications()
+
+    const { listen } = await import('@tauri-apps/api/event')
+    const { openPip } = usePipWindow()
+    unlistenPipOpen = await listen<number>('pip:open', (event) => {
+      openPip(event.payload)
+    })
   }
 
   // Connect centralized session state WS
@@ -488,6 +497,7 @@ async function sendTestNotification() {
 onUnmounted(() => {
   document.removeEventListener('mousemove', trackMouse)
   document.removeEventListener('keydown', handleGlobalKeydown)
+  unlistenPipOpen?.()
   destroyTorch()
   disconnectApproval()
   destroySessionStateWS()