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 />

tests/unit/App.test.tsx

@@ -6,6 +6,8 @@ import { render, screen, fireEvent, cleanup, waitFor } from '@testing-library/re
 vi.mock('../../src/renderer/inbox/api.js', () => ({
   inboxApi: {
     listNotes: vi.fn(async () => []),
+    listByStatus: vi.fn(async () => []),
+    countsByStatus: vi.fn(async () => ({ active: 0, completed: 0, archived: 0, trashed: 0 })),
     getContinuity: vi.fn(async () => ({
       weekStart: '', weekCount: 0, weekTarget: 7,
       consecutiveCompleteWeeks: 0, showRecoveryToast: false, lastNoteAt: null
@@ -58,7 +60,12 @@ import { inboxApi } from '../../src/renderer/inbox/api.js';
 describe('App — settings view', () => {
   beforeEach(() => {
     cleanup();
-    useInbox.setState({ showSettings: false, notes: [], trashNotes: [], trashCount: 0 });
+    useInbox.setState({
+      view: 'inbox',
+      counts: { active: 0, completed: 0, archived: 0, trashed: 0 },
+      showSettings: false, showTrash: false,
+      notes: [], trashNotes: [], trashCount: 0
+    });
   });
 
   it('renders SettingsPage when showSettings=true', async () => {
@@ -89,3 +96,38 @@ describe('App — settings view', () => {
     await waitFor(() => expect(useInbox.getState().showSettings).toBe(true));
   });
 });
+
+describe('App header — 4 tabs', () => {
+  beforeEach(() => {
+    cleanup();
+    useInbox.setState({
+      view: 'inbox',
+      counts: { active: 5, completed: 3, archived: 2, trashed: 1 },
+      notes: [], trashNotes: [], trashCount: 0,
+      showTrash: false, showSettings: false
+    });
+  });
+
+  it('renders 4 tabs with counts', () => {
+    render(<App />);
+    expect(screen.getByRole('button', { name: /Inbox\(5\)/ })).toBeInTheDocument();
+    expect(screen.getByRole('button', { name: /완료\(3\)/ })).toBeInTheDocument();
+    expect(screen.getByRole('button', { name: /보관\(2\)/ })).toBeInTheDocument();
+    expect(screen.getByRole('button', { name: /휴지통\(1\)/ })).toBeInTheDocument();
+  });
+
+  it('clicking 완료 tab sets view=completed', () => {
+    render(<App />);
+    fireEvent.click(screen.getByRole('button', { name: /완료/ }));
+    expect(useInbox.getState().view).toBe('completed');
+  });
+
+  it('aria-pressed reflects current view', () => {
+    useInbox.setState({ view: 'archived' });
+    render(<App />);
+    const archivedBtn = screen.getByRole('button', { name: /보관/ });
+    expect(archivedBtn.getAttribute('aria-pressed')).toBe('true');
+    const inboxBtn = screen.getByRole('button', { name: /Inbox/ });
+    expect(inboxBtn.getAttribute('aria-pressed')).toBe('false');
+  });
+});