feat(ui): rewarded-ad grant for an empty booster

Tapping an empty booster opens the get-one dialog; confirming watches a
rewarded ad and, on earn, grants +1 of that booster and logs booster_granted
(source: ad). Covered by a widget test using an uninitialized AdService whose
showRewarded() resolves true.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

lib/ui/screens/game_screen.dart

@@ -206,11 +206,10 @@ class _GameScreenState extends ConsumerState<GameScreen>
     );
   }
 
-  /// An empty booster offers to get one. The rewarded-ad grant is wired in
-  /// Task 15.
+  /// Task 15: an empty booster offers a rewarded ad; on reward, grant +1.
   Future<void> _offerBoosterAd(BoosterType type) async {
     final l10n = AppLocalizations.of(context)!;
-    await showDialog<bool>(
+    final confirmed = await showDialog<bool>(
       context: context,
       builder: (context) => AlertDialog(
         content: Text(l10n.boosterGetWithAd),
@@ -226,6 +225,14 @@ class _GameScreenState extends ConsumerState<GameScreen>
         ],
       ),
     );
+    if (confirmed != true) return;
+    final earned = await ref.read(adServiceProvider).showRewarded();
+    if (earned) {
+      await ref.read(boosterInventoryProvider.notifier).grant(type, 1);
+      ref
+          .read(analyticsProvider)
+          .boosterGranted(type: type.name, count: 1, source: 'ad');
+    }
   }
 
   @override