feat(web/m7-381): admin overview Library Scan section + manual trigger

Adds getScanStatus/triggerScan helpers, createScanStatusQuery factory
(3s poll), qk.scanStatus(), and a Library Scan section on the admin
overview page with per-stage tallies and inline Run scan button.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

web/src/lib/api/admin.scan.test.ts

@@ -0,0 +1,28 @@
+import { describe, it, expect, vi, beforeEach } from 'vitest';
+import { getScanStatus, triggerScan } from './admin';
+
+vi.mock('./client', () => ({
+  api: { get: vi.fn(), post: vi.fn() }
+}));
+
+import { api } from './client';
+
+describe('admin scan API', () => {
+  beforeEach(() => vi.clearAllMocks());
+
+  it('getScanStatus GETs the correct path', async () => {
+    (api.get as unknown as ReturnType<typeof vi.fn>).mockResolvedValueOnce({
+      id: 's1', started_at: '2026-05-04T00:00:00Z', finished_at: null, in_flight: true
+    });
+    const got = await getScanStatus();
+    expect(api.get).toHaveBeenCalledWith('/api/admin/scan/status');
+    expect(got.in_flight).toBe(true);
+  });
+
+  it('triggerScan POSTs an empty body to /run', async () => {
+    (api.post as unknown as ReturnType<typeof vi.fn>).mockResolvedValueOnce({ id: 's2' });
+    const got = await triggerScan();
+    expect(api.post).toHaveBeenCalledWith('/api/admin/scan/run', {});
+    expect(got.id).toBe('s2');
+  });
+});