fix: hide spent rescue to prevent StateError crash; log per-attempt starts

Expose engine.rescueUsed getter and surface it through GameViewState so
the result overlay can omit the watch-ad FilledButton after a rescue has
been consumed, preventing a second tap from calling useContinue /
addExtraMoves and hitting their StateError guard. Give-up is promoted to
FilledButton when rescue is unavailable for clear affordance.

Also emit stageStart / endlessStart analytics in restart() so every
attempt (not just the first) is bracketed by a matching start event.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

lib/game/engine/game_engine.dart

@@ -82,6 +82,7 @@ class GameEngine {
   List<Objective> get objectives => List.unmodifiable(_objectives);
   GamePhase get phase => _phase;
   StuckReason? get stuckReason => _stuckReason;
+  bool get rescueUsed => _rescueUsed;
 
   int get starsEarned => _phase == GamePhase.won
       ? _stage.stars.starsFor(movesLeft: movesLeft)

lib/state/game_session_notifier.dart

@@ -6,6 +6,7 @@ import '../game/models/grid.dart';
 import '../game/models/objective.dart';
 import '../game/models/piece.dart';
 import '../game/models/stage.dart';
+import 'providers.dart';
 
 /// Immutable snapshot of one engine moment; the only game state the UI sees.
 class GameViewState {
@@ -24,6 +25,7 @@ class GameViewState {
     required this.lastPlacement,
     required this.fxTick,
     required this.endless,
+    required this.rescueUsed,
   });
 
   final GridState grid;
@@ -43,6 +45,7 @@ class GameViewState {
   final int fxTick;
 
   final bool endless;
+  final bool rescueUsed;
 }
 
 /// Bridges the pure-Dart [GameEngine] to the widget tree. The engine object
@@ -72,6 +75,17 @@ class GameSessionNotifier extends Notifier<GameViewState?> {
     final stage = _stage;
     if (stage == null) throw StateError('no stage to restart');
     startStage(stage, attempt: _attempt + 1, generator: _generatorOverride);
+    if (stage.endless) {
+      ref.read(analyticsProvider).endlessStart();
+    } else {
+      final flow = ref.read(seasonFlowProvider);
+      if (flow != null) {
+        ref.read(analyticsProvider).stageStart(
+              seasonId: flow.pack.seasonId,
+              stageId: flow.stage.id,
+            );
+      }
+    }
   }
 
   bool tryPlace(int trayIndex, int x, int y) {
@@ -119,6 +133,7 @@ class GameSessionNotifier extends Notifier<GameViewState?> {
       objectiveProgress: engine.objectiveProgress,
       lastPlacement: lastPlacement,
       fxTick: _fxTick,
+      rescueUsed: engine.rescueUsed,
     );
   }
 }

lib/ui/screens/game_screen.dart

@@ -391,33 +391,47 @@ class _GameScreenState extends ConsumerState<GameScreen>
       (GamePhase.stuck, StuckReason.outOfMoves) => (
           l10n.outOfMoves,
           [
-            FilledButton(
-              onPressed: () {
-                ref.read(analyticsProvider).rescueUsed(type: 'extra_moves');
-                notifier.addExtraMoves();
-              },
-              child: Text(l10n.plusFiveMoves),
-            ),
-            TextButton(
-              onPressed: notifier.declineAndLose,
-              child: Text(l10n.giveUp),
-            ),
+            if (!view.rescueUsed)
+              FilledButton(
+                onPressed: () {
+                  ref.read(analyticsProvider).rescueUsed(type: 'extra_moves');
+                  notifier.addExtraMoves();
+                },
+                child: Text(l10n.plusFiveMoves),
+              ),
+            if (view.rescueUsed)
+              FilledButton(
+                onPressed: notifier.declineAndLose,
+                child: Text(l10n.giveUp),
+              )
+            else
+              TextButton(
+                onPressed: notifier.declineAndLose,
+                child: Text(l10n.giveUp),
+              ),
           ],
         ),
       (GamePhase.stuck, _) => (
           l10n.boardFull,
           [
-            FilledButton(
-              onPressed: () {
-                ref.read(analyticsProvider).rescueUsed(type: 'continue');
-                notifier.useContinue();
-              },
-              child: Text(l10n.watchAdContinue),
-            ),
-            TextButton(
-              onPressed: notifier.declineAndLose,
-              child: Text(l10n.giveUp),
-            ),
+            if (!view.rescueUsed)
+              FilledButton(
+                onPressed: () {
+                  ref.read(analyticsProvider).rescueUsed(type: 'continue');
+                  notifier.useContinue();
+                },
+                child: Text(l10n.watchAdContinue),
+              ),
+            if (view.rescueUsed)
+              FilledButton(
+                onPressed: notifier.declineAndLose,
+                child: Text(l10n.giveUp),
+              )
+            else
+              TextButton(
+                onPressed: notifier.declineAndLose,
+                child: Text(l10n.giveUp),
+              ),
           ],
         ),
       (GamePhase.lost, _) when view.endless => (

test/game/engine/game_engine_test.dart

@@ -193,6 +193,21 @@ void main() {
     });
   });
 
+  group('rescueUsed getter', () {
+    test('rescueUsed flag is exposed and flips after a rescue', () {
+      final engine = GameEngine(
+        _stage(moveLimit: 1),
+        generator: _smallPool(1),
+      );
+      expect(engine.rescueUsed, isFalse);
+      engine.tryPlace(0, 0, 0);
+      expect(engine.phase, GamePhase.stuck);
+      expect(engine.rescueUsed, isFalse);
+      engine.addExtraMoves();
+      expect(engine.rescueUsed, isTrue);
+    });
+  });
+
   group('dead board and continue', () {
     StageConfig deadStage() {
       // Checkerboard: only monos fit, and the injected pool has none small