feat(v029): 헤더 4탭 (Inbox/완료/보관/휴지통) + count badge

- App.tsx: 기존 2탭 (Inbox/휴지통) → 4탭. setView/counts 사용.
- onNavigate 도 setView 로 위임 (mirror state 동기 갱신).
- App.test: 4탭 렌더 + 클릭 → setView('completed') + aria-pressed (3 cases).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/renderer/inbox/App.tsx

@@ -23,6 +23,10 @@ export function App(): React.ReactElement {
   } = useInbox();
   const showSettings = useInbox((s) => s.showSettings);
   const setShowSettings = useInbox((s) => s.setShowSettings);
+  // v0.2.9 Cut B Task 5 — 4탭 (Inbox/완료/보관/휴지통).
+  const view = useInbox((s) => s.view);
+  const counts = useInbox((s) => s.counts);
+  const setView = useInbox((s) => s.setView);
   const [recoveryDismissed, setRecoveryDismissed] = useState(isRecoveryDismissedToday());
 
   useEffect(() => {
@@ -35,15 +39,8 @@ export function App(): React.ReactElement {
       useInbox.setState({ ollamaStatus: status });
     });
     const unsubNav = inboxApi.onNavigate((view) => {
-      if (view === 'settings') {
-        useInbox.getState().setShowSettings(true);
-      } else if (view === 'inbox') {
-        useInbox.getState().setShowSettings(false);
-        if (useInbox.getState().showTrash) void useInbox.getState().toggleShowTrash();
-      } else if (view === 'trash') {
-        useInbox.getState().setShowSettings(false);
-        if (!useInbox.getState().showTrash) void useInbox.getState().toggleShowTrash();
-      }
+      // v0.2.9 Cut B Task 4 — setView 가 mirror state (showTrash/showSettings) 동기 갱신.
+      useInbox.getState().setView(view);
     });
     const onFocus = () => { void refreshMeta(); };
     window.addEventListener('focus', onFocus);
@@ -72,20 +69,23 @@ export function App(): React.ReactElement {
       <div className="header">
         <h1 style={{ fontSize: 18, margin: 0 }}>Inkling</h1>
         <div style={{ display: 'flex', gap: 6, marginLeft: 12 }}>
-          <button
-            onClick={() => { if (showTrash) void toggleShowTrash(); }}
-            aria-pressed={!showTrash}
-            style={tabBtnStyle(!showTrash)}
-          >
-            Inbox({notes.length})
-          </button>
-          <button
-            onClick={() => { if (!showTrash) void toggleShowTrash(); }}
-            aria-pressed={showTrash}
-            style={tabBtnStyle(showTrash)}
-          >
-            휴지통({trashCount})
-          </button>
+          {(
+            [
+              { key: 'inbox', label: 'Inbox', count: counts.active },
+              { key: 'completed', label: '완료', count: counts.completed },
+              { key: 'archived', label: '보관', count: counts.archived },
+              { key: 'trash', label: '휴지통', count: counts.trashed }
+            ] as const
+          ).map((t) => (
+            <button
+              key={t.key}
+              onClick={() => setView(t.key)}
+              aria-pressed={view === t.key}
+              style={tabBtnStyle(view === t.key)}
+            >
+              {t.label}({t.count})
+            </button>
+          ))}
         </div>
         <div style={{ display: 'flex', flexDirection: 'column', alignItems: 'flex-end', gap: 2, marginLeft: 'auto' }}>
           <ContinuityBadge />