refactor(engine): first ambiguity burn-down batch — 302 → 198 pairs

Two structural fixes from the #143 backlog:

- Game-state ordering spine: the three pre-mutation GameStateResource
  writers (tick_elapsed_time, sync_settings_to_game,
  handle_restore_prompt) are now a deterministic chain before
  GameMutation, and the remaining unordered readers
  (update_selection_hud, handle_hint_button, tick_hint_highlight,
  handle_right_click, snap_cards_on_window_resize,
  sync_pile_marker_visibility, auto_save_game_state) are ordered after
  it. Readers now see the current frame's moves deterministically
  instead of racing the mutators.

- NewGameRequestWriters set: every in-cluster writer of
  NewGameRequestEvent (buttons, modals, mode picker, seed poller,
  restore prompt) is registered in a shared set marked ambiguous with
  itself — writer-vs-writer append order is meaningless since consumers
  drain the whole queue. Out-of-cluster writers (home, challenge,
  time-attack, win-summary, play-by-seed, difficulty, stats plugins)
  can join the set when the test cluster grows.

AMBIGUITY_BASELINE ratchets 302 → 198. Remaining backlog is dominated
by the Sprite (72) / Transform (48) visual-domain cluster, which needs
per-domain set architecture — next batch.

Refs #143

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

solitaire_engine/src/game_plugin/mod.rs

@@ -63,6 +63,18 @@ pub struct GameOverScreen;
 #[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
 pub struct GameMutation;
 
+/// System set for every writer of [`crate::events::NewGameRequestEvent`].
+///
+/// Many UI entry points fire this trigger (buttons, keyboard, modals,
+/// mode pickers). Their relative append order within a frame is
+/// meaningless — consumers drain the whole queue — so members are
+/// registered `.in_set(NewGameRequestWriters).ambiguous_with(NewGameRequestWriters)`
+/// to declare writer-vs-writer order irrelevant instead of leaving it as an
+/// ambiguity (#143). Only ever combine with `.ambiguous_with` on the same
+/// set; do NOT hang ordering edges off this set.
+#[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
+pub struct NewGameRequestWriters;
+
 /// Persistence path for the in-progress game state file. `None` disables I/O.
 #[derive(Resource, Debug, Clone)]
 pub struct GameStatePath(pub Option<PathBuf>);
@@ -208,7 +220,13 @@ impl Plugin for GamePlugin {
             .add_message::<AppLifecycle>()
             // add_message is idempotent; SettingsPlugin also registers this.
             .add_message::<crate::settings_plugin::SettingsChangedEvent>()
-            .add_systems(Update, poll_pending_new_game_seed.before(GameMutation))
+            .add_systems(
+                Update,
+                poll_pending_new_game_seed
+                    .before(GameMutation)
+                    .in_set(NewGameRequestWriters)
+                    .ambiguous_with(NewGameRequestWriters),
+            )
             .add_systems(
                 Update,
                 (handle_new_game, handle_draw, handle_move, handle_undo)
@@ -217,19 +235,40 @@ impl Plugin for GamePlugin {
             )
             .add_systems(Update, check_no_moves.after(GameMutation))
             .add_systems(Update, record_replay_on_win.after(GameMutation))
-            .add_systems(Update, handle_confirm_input.after(GameMutation))
-            .add_systems(Update, handle_confirm_button_input.after(GameMutation))
-            .add_systems(Update, handle_game_over_input.after(GameMutation))
-            .add_systems(Update, handle_game_over_button_input.after(GameMutation))
+            .add_systems(
+                Update,
+                (
+                    handle_confirm_input,
+                    handle_confirm_button_input,
+                    handle_game_over_input,
+                    handle_game_over_button_input,
+                )
+                    .after(GameMutation)
+                    .in_set(NewGameRequestWriters)
+                    .ambiguous_with(NewGameRequestWriters),
+            )
             // Restore prompt: spawn the modal once the splash is gone,
             // route Continue / New Game intents back into the existing
             // GameMutation flow.
             .add_systems(Update, spawn_restore_prompt_if_pending)
-            .add_systems(Update, handle_restore_prompt.before(GameMutation))
-            .add_systems(Update, sync_settings_to_game.before(GameMutation))
+            // All three pre-mutation game-state writers are chained: elapsed
+            // time ticks first, settings sync next, then the restore prompt —
+            // a deterministic spine instead of three unordered ResMut holders
+            // (ambiguity burn-down, #143).
+            .add_systems(
+                Update,
+                (
+                    tick_elapsed_time,
+                    sync_settings_to_game,
+                    handle_restore_prompt
+                        .in_set(NewGameRequestWriters)
+                        .ambiguous_with(NewGameRequestWriters),
+                )
+                    .chain()
+                    .before(GameMutation),
+            )
             .init_resource::<AutoSaveTimer>()
-            .add_systems(Update, tick_elapsed_time)
-            .add_systems(Update, auto_save_game_state)
+            .add_systems(Update, auto_save_game_state.after(GameMutation))
             .add_systems(Last, save_game_state_on_exit);
     }
 }