fix(boosters): address final-review findings

- daily claim: record the claim before granting boosters, so a crash
  mid-claim forfeits at most one reward instead of allowing a re-claim
  (booster farming) on next launch.
- game screen: disarm the booster target synchronously before awaiting,
  so a rapid second board tap can't double-fire a use or stack a dialog.
- new players: seed one of each booster once (idempotent persisted flag),
  fulfilling the spec's starting inventory. Wired in main().

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

lib/ui/screens/game_screen.dart

@@ -169,10 +169,13 @@ class _GameScreenState extends ConsumerState<GameScreen>
     final y = (local.dy / cell).floor();
     if (x < 0 || x >= GridState.size || y < 0 || y >= GridState.size) return;
 
+    // Disarm synchronously, before any await, so a rapid second tap on the
+    // board is a no-op rather than a redundant booster use / stacked dialog.
+    setState(() => _arming = null);
+
     final session = ref.read(gameSessionProvider.notifier);
     if (armed == BoosterType.hammer) {
       await session.useHammer(x, y);
-      if (mounted) setState(() => _arming = null);
     } else if (armed == BoosterType.lineBomb) {
       final axis = await _chooseLineAxis();
       if (axis == _LineAxis.row) {
@@ -180,8 +183,6 @@ class _GameScreenState extends ConsumerState<GameScreen>
       } else if (axis == _LineAxis.col) {
         await session.useLineBomb(col: x);
       }
-      // A dismissed chooser cancels the use but still clears the armed state.
-      if (mounted) setState(() => _arming = null);
     }
   }