feat(sync): follow the visit sync on the dashboard

Show the "Syncing with Steam" badge while a visit sync runs, then
reload the sync changes banner and the library.

src/pages/Dashboard.test.jsx

@@ -6,7 +6,10 @@ import {fetchRoutes, json} from '../test/fetchRoutes.js';
 import {renderWithProviders} from '../test/renderWithProviders.jsx';
 
 vi.mock('react-i18next', () => import('../test/i18n-mock.js'));
-vi.mock('../hooks/useLibrarySync.js', () => ({default: () => ({status: 'OK', lastSyncedAt: null, isRunning: false})}));
+const watchSync = vi.hoisted(() => vi.fn());
+vi.mock('../hooks/useLibrarySync.js', () => ({
+    default: () => ({status: 'OK', lastSyncedAt: null, isRunning: false, watch: watchSync}),
+}));
 vi.mock('../hooks/useForceSync.js', () => ({default: () => ({trigger: vi.fn(), busy: false})}));
 
 const avatar = 'https://avatars.steamstatic.com/abc_full.jpg';
@@ -42,6 +45,7 @@ beforeEach(() => {
 });
 
 afterEach(() => {
+    watchSync.mockClear();
     cleanup();
     localStorage.clear();
 });
@@ -177,5 +181,22 @@ describe('Dashboard', () => {
 
         expect(await screen.findByText(/DASHBOARD.HELLO/)).toBeTruthy();
     });
-});
 
+    it('watches the sync the server started for this visit', async () => {
+        fetchRoutes({
+            ...dashboardRoutes(),
+            'GET /api/library/games-count': json(200, {count: 1, hasSteamId: true, syncStarted: true}),
+        });
+        renderDashboard();
+
+        await waitFor(() => expect(watchSync).toHaveBeenCalledTimes(1));
+    });
+
+    it('does not watch a sync when the server started none', async () => {
+        fetchRoutes(dashboardRoutes());
+        renderDashboard();
+
+        expect(await screen.findByText(/DASHBOARD.HELLO/)).toBeTruthy();
+        expect(watchSync).not.toHaveBeenCalled();
+    });
+});