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)

frontend/src/composables/usePipWindow.ts

@@ -0,0 +1,123 @@
+import { ref } from 'vue'
+import { isTauri, getTauriStore } from '@/lib/tauri'
+import { trackLoading } from '@/lib/loadingWindow'
+
+const STORE_KEY_PREFIX = 'pipWindow.geometry.'
+
+interface WindowGeometry {
+  x: number
+  y: number
+  width: number
+  height: number
+}
+
+const pipWindows = ref<Map<number, boolean>>(new Map())
+
+async function loadGeometry(idx: number): Promise<WindowGeometry | null> {
+  try {
+    const store = await getTauriStore()
+    return await store.get<WindowGeometry>(`${STORE_KEY_PREFIX}${idx}`) ?? null
+  } catch {
+    return null
+  }
+}
+
+async function saveGeometry(idx: number, geo: WindowGeometry): Promise<void> {
+  try {
+    const store = await getTauriStore()
+    await store.set(`${STORE_KEY_PREFIX}${idx}`, geo)
+  } catch {}
+}
+
+export function usePipWindow() {
+  async function openPip(terminalIndex: number): Promise<boolean> {
+    if (!isTauri) return false
+
+    const pipLabel = `pip-terminal-${terminalIndex}`
+
+    try {
+      const { WebviewWindow } = await import('@tauri-apps/api/webviewWindow')
+
+      const existing = await WebviewWindow.getByLabel(pipLabel)
+      if (existing) {
+        await existing.setFocus()
+        return true
+      }
+
+      const pipUrl = `/transcript-debug/${terminalIndex}?pip=1`
+
+      // Restore last position/size or use defaults
+      const saved = await loadGeometry(terminalIndex)
+      const x = saved?.x ?? (window.screen.width - 400)
+      const y = saved?.y ?? (60 + (terminalIndex - 1) * 40)
+      const width = saved?.width ?? 380
+      const height = saved?.height ?? 620
+
+      // Track in the shared loading indicator (bottom-right spinner)
+      const dismissLoading = await trackLoading(pipLabel)
+
+      // Create real window hidden
+      const pip = new WebviewWindow(pipLabel, {
+        url: pipUrl,
+        title: `T${terminalIndex} - Agent UI`,
+        width,
+        height,
+        x,
+        y,
+        visible: false,
+        alwaysOnTop: false,
+        decorations: false,
+        resizable: true,
+        focus: true,
+      })
+
+      pipWindows.value.set(terminalIndex, true)
+
+      // When real window is ready: show it, remove from loading tracker
+      pip.once('tauri://webview-created', () => {
+        setTimeout(async () => {
+          try { await pip.show() } catch {}
+          try { await pip.setFocus() } catch {}
+          await dismissLoading()
+        }, 200)
+      })
+
+      // Persist geometry on close
+      pip.onCloseRequested(async () => {
+        try {
+          const pos = await pip.outerPosition()
+          const size = await pip.outerSize()
+          await saveGeometry(terminalIndex, {
+            x: pos.x,
+            y: pos.y,
+            width: size.width,
+            height: size.height,
+          })
+        } catch {}
+        pipWindows.value.delete(terminalIndex)
+      })
+
+      return true
+    } catch (e) {
+      console.warn(`Failed to open PiP window for T${terminalIndex}:`, e)
+      pipWindows.value.delete(terminalIndex)
+      return false
+    }
+  }
+
+  async function closePip(terminalIndex: number): Promise<void> {
+    const pipLabel = `pip-terminal-${terminalIndex}`
+    try {
+      const { WebviewWindow } = await import('@tauri-apps/api/webviewWindow')
+      const existing = await WebviewWindow.getByLabel(pipLabel)
+      if (existing) await existing.close()
+    } catch {}
+    pipWindows.value.delete(terminalIndex)
+  }
+
+  function isPipOpen(terminalIndex: number): boolean {
+    return pipWindows.value.get(terminalIndex) ?? false
+  }
+
+  return { openPip, closePip, isPipOpen, pipWindows }
+}