feat(admin): show paused sessions in live view; reset to live on logout

- Live cards freeze the worked timer at paused_at and show an amber
  "Gepauzeerd" badge plus a "Pauze H:MM:SS" total when paused.
- AuthContext.signOut resets the path to / so the next admin login lands
  on Live rather than the tab it logged out from.

apps/admin/src/auth/AuthContext.test.tsx

@@ -92,4 +92,23 @@ describe('AuthContext admin gate', () => {
     expect(getToken()).toBeNull();
     expect(screen.getByTestId('authed')).toHaveTextContent('false');
   });
+
+  it('signOut resets the path to / so the next login lands on Live', async () => {
+    mockedFetchMe.mockResolvedValue({
+      user: { id: 'a1', email: 'admin@solelog.local', name: 'Admin', role: 'admin' },
+    });
+    window.history.replaceState(null, '', '/activities');
+    expect(window.location.pathname).toBe('/activities');
+
+    const user = userEvent.setup();
+    renderHarness();
+    await user.click(screen.getByRole('button', { name: 'go' }));
+    await waitFor(() => expect(screen.getByTestId('authed')).toHaveTextContent('true'));
+
+    await user.click(screen.getByRole('button', { name: 'uit' }));
+
+    await waitFor(() => expect(screen.getByTestId('authed')).toHaveTextContent('false'));
+    expect(window.location.pathname).toBe('/');
+    expect(getToken()).toBeNull();
+  });
 });

apps/admin/src/auth/AuthContext.tsx

@@ -34,6 +34,9 @@ export function AuthProvider({ children }: { children: ReactNode }) {
   }, []);
 
   const signOut = useCallback(() => {
+    // Reset the path to / so the next authed mount lands on Live, not whatever tab
+    // (e.g. Account/Activities) the admin happened to log out from.
+    window.history.replaceState(null, '', '/');
     clearToken();
     setIsAuthed(false);
   }, []);