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/hud_plugin/mod.rs

@@ -36,7 +36,7 @@ use crate::events::{
     UndoRequestEvent, WinStreakMilestoneEvent,
 };
 use crate::font_plugin::FontResource;
-use crate::game_plugin::GameMutation;
+use crate::game_plugin::{GameMutation, NewGameRequestWriters};
 #[cfg(target_os = "android")]
 use crate::input_plugin::TouchDragSet;
 use crate::layout::HUD_BAND_HEIGHT;
@@ -478,10 +478,12 @@ impl Plugin for HudPlugin {
             .add_systems(Update, announce_auto_complete.after(GameMutation))
             .add_systems(
                 Update,
-                update_selection_hud.run_if(
-                    resource_exists_and_changed::<SelectionState>
-                        .or(resource_exists_and_changed::<GameStateResource>),
-                ),
+                update_selection_hud
+                    .after(GameMutation)
+                    .run_if(
+                        resource_exists_and_changed::<SelectionState>
+                            .or(resource_exists_and_changed::<GameStateResource>),
+                    ),
             )
             .add_systems(Update, update_hud_typography)
             .add_systems(
@@ -503,13 +505,17 @@ impl Plugin for HudPlugin {
             .add_systems(
                 Update,
                 (
-                    handle_new_game_button,
+                    handle_new_game_button
+                        .in_set(NewGameRequestWriters)
+                        .ambiguous_with(NewGameRequestWriters),
                     handle_undo_button,
                     handle_pause_button,
                     handle_help_button,
-                    handle_hint_button,
+                    handle_hint_button.after(GameMutation),
                     handle_modes_button,
-                    handle_mode_option_click,
+                    handle_mode_option_click
+                        .in_set(NewGameRequestWriters)
+                        .ambiguous_with(NewGameRequestWriters),
                     handle_modes_backdrop_click,
                     close_modes_popover_on_escape,
                     handle_menu_button,