feat: video letterboxing, card badge styling, component updates

- Add object-fit: contain + black background for video in DTMediaFrame
- Style .dt-card-badge with mode-colored background, padding, and
  bevel-aware positioning (negative right offset for clean diagonal clip)
- Restore DTStaggerContainer in react-native (was incorrectly deleted)
- Update DTGallery, DTModal, DTMobileFilterOverlay, DTMediaFrame components
- Refresh showcase pages for desktop and mobile

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

packages/showcase/mobile/src/screens/HomeScreen.tsx

@@ -58,14 +58,14 @@ const categories: {
   },
   {
     title: 'ADVANCED CARDS',
-    subtitle: 'Selected state, progress bar, badge overlays, stagger',
+    subtitle: 'Selected state, progress bar, badge overlays',
     mode: 'emphasis',
     route: 'CardsAdvanced',
     count: 4,
   },
   {
     title: 'ANIMATIONS',
-    subtitle: 'DTStaggerContainer, useScaleIn, usePulse',
+    subtitle: 'useScaleIn, usePulse',
     mode: 'success',
     route: 'Animations',
     count: 3,