refactor: unify dashboard/terminal selector into single strip, default to dashboard

Remove separate Chat/SE tab toggle. Dashboard is now a button in the
terminal strip alongside T1-T5. Chat only renders when a specific
terminal route is active (/transcript-debug/:n).

frontend/src/pages/TranscriptDebugPage.vue

@@ -4,7 +4,7 @@ import { useRoute, useRouter } from 'vue-router'
 import { useTranscriptDebug } from '@/composables/transcript-debug'
 import { useVoiceInput } from '@/composables/useVoiceInput'
 import { useSessionState } from '@/stores/session-state'
-import { ChatContainer, AquaticBackground, AgentBadge, NewSessionModal } from '@/components/transcript-debug'
+import { ChatContainer, AquaticBackground, AgentBadge, NewSessionModal, SyncEnginePanel } from '@/components/transcript-debug'
 import type { AgentName } from '@/types/transcript-debug'
 import { isTauri, isMobileTauri, getTauriWindow } from '@/lib/tauri'
 import { usePipWindow } from '@/composables/usePipWindow'
@@ -63,6 +63,9 @@ const showSelector = ref(false)
 const showNewSessionModal = ref(false)
 const isPipWindow = computed(() => route.query.pip === '1')
 
+// Dashboard vs terminal view — driven by route
+const isDashboard = computed(() => !route.params.terminalIndex)
+
 // Readability overlay
 const savedOverlay = localStorage.getItem('transcript-overlay-opacity')
 const overlayOpacity = ref(savedOverlay !== null ? parseFloat(savedOverlay) : 0.55)
@@ -136,6 +139,10 @@ async function handleModalCreateNew(agent: AgentName, initialPrompt: string) {
   }
 }
 
+function goToDashboard() {
+  router.push({ name: 'transcript-debug' })
+}
+
 function handleTerminalSwitch(sessionId: string) {
   const idx = sessionState.terminalRegistry.findIndex(
     e => e.transcriptSessionId === sessionId
@@ -219,6 +226,15 @@ onMounted(async () => {
   await init()
   await voice.init()
   syncTerminalFromRoute()
+
+  // Signal to the parent window that this PiP page is ready to show
+  if (isTauri && route.query.pip === '1') {
+    try {
+      const { getCurrentWebviewWindow } = await import('@tauri-apps/api/webviewWindow')
+      const { emitTo } = await import('@tauri-apps/api/event')
+      await emitTo('main', 'pip:ready', getCurrentWebviewWindow().label)
+    } catch {}
+  }
 })
 
 onBeforeUnmount(() => {
@@ -252,13 +268,23 @@ onBeforeUnmount(() => {
     <!-- Terminal selector strip (hidden in PiP) -->
     <div v-if="!isPipWindow" class="terminal-strip">
       <div class="strip-left">
+        <button
+          :class="['strip-terminal-btn', 'strip-dashboard-btn', { active: isDashboard }]"
+          @click="goToDashboard"
+          title="Dashboard"
+        >
+          <svg width="10" height="10" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5">
+            <rect x="3" y="3" width="7" height="7" rx="1"/><rect x="14" y="3" width="7" height="7" rx="1"/>
+            <rect x="3" y="14" width="7" height="7" rx="1"/><rect x="14" y="14" width="7" height="7" rx="1"/>
+          </svg>
+        </button>
         <button
           v-for="(entry, idx) in sessionState.terminalRegistry"
           :key="entry.transcriptSessionId"
           :class="[
             'strip-terminal-btn',
             {
-              active: String(idx + 1) === route.params.terminalIndex || (!route.params.terminalIndex && entry.transcriptSessionId === activeTerminalSessionId),
+              active: String(idx + 1) === route.params.terminalIndex,
               dead: !entry.alive
             }
           ]"
@@ -360,6 +386,8 @@ onBeforeUnmount(() => {
         </div>
       </Transition>
 
+      <!-- Terminal chat (only when a specific terminal is selected) -->
+      <template v-if="!isDashboard">
         <ChatContainer
           ref="chatRef"
           v-if="conversation"
@@ -410,6 +438,10 @@ onBeforeUnmount(() => {
           <small v-if="!sessionState.terminalRegistry.length">No terminals registered</small>
           <small v-else>Select a terminal above to begin</small>
         </div>
+      </template>
+
+      <!-- Dashboard (default view) -->
+      <SyncEnginePanel v-if="isDashboard" />
     </div>
 
     <!-- New session modal -->
@@ -499,6 +531,16 @@ onBeforeUnmount(() => {
   gap: 0.5rem;
 }
 
+.strip-dashboard-btn {
+  gap: 0;
+}
+.strip-dashboard-btn svg {
+  opacity: 0.7;
+}
+.strip-dashboard-btn.active svg {
+  opacity: 1;
+}
+
 .realtime-dot {
   color: var(--text-muted);
   opacity: 0.4;
@@ -641,6 +683,13 @@ onBeforeUnmount(() => {
    ChatContainer glass-transparent overrides (mirrored from FloatingTranscriptDebug)
    ══════════════════════════════════════════════════════════════════════════════ */
 
+.content-area :deep(.sync-engine-panel) {
+  position: relative;
+  z-index: 1;
+  flex: 1;
+  overflow-y: auto;
+}
+
 .content-area :deep(.chat-container) {
   background: transparent !important;
   border: none !important;