refactor(engine): ambiguity gate covers the full cluster — batches 1-3, 585 pairs burned to zero

Port the July 7 gate-extender branch onto current master (the You-hub,
touch action bar, glass tab bar, Phase L, and hint-ghost work all landed
since) and finish batch 3. cluster_app now includes the mode, replay,
input, radial, tooltip, cursor, touch-selection, and safe-area plugins on
top of batches 1-2; the 585 ambiguous pairs the expansion exposed are
annotated down to zero and the gate stays assert_eq!(count, 0).

New ordering machinery:
- ReplayPlayback: playback driver chain on the pre-mutation spine
  (PointerInput < ReplayPlayback < overlay chain < GameMutation)
- ModeStart: mode-start handlers between the stats abandon-recorder and
  GameMutation; ChallengeCompletion < DailyCompletion < WeeklyGoalsEval
  pinned inside ProgressUpdate so `.after(ProgressUpdate)` readers see
  settled progress
- PointerInput: public set wrapping the input chain; AbandonRecord on the
  stats abandon-recorder; PendingHint around the async hint pipeline;
  HintGhostFx for the ghost chain (after the full visual spine)
- Clubs: MoveRequestWriters, WarningToastWriters join the existing
  request/toast writer clubs; UiTextFx grows the overlay/tooltip/safe-area
  chrome painters; SettingsAccess grows the lag-tolerant settings readers

Gate: cargo test --workspace green (993 engine tests), clippy
--all-targets -D warnings clean, rustfmt applied.

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

solitaire_engine/src/settings_plugin/mod.rs

@@ -87,6 +87,19 @@ pub struct SettingsChangedEvent(pub Settings);
 #[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
 pub struct SettingsMutation;
 
+/// Self-ambiguous club for the screen/overlay systems that touch
+/// [`SettingsResource`] (onboarding first-run flag, home difficulty/draw
+/// chips, leaderboard opt-in and display name, pause draw toggle, splash
+/// reduce-motion reads, …). Each accessor touches its own disjoint fields,
+/// and the modal-stacking guard means at most one of these screens is
+/// interactive at a time — same-frame access order is provably irrelevant,
+/// so members declare `.in_set(SettingsAccess).ambiguous_with(SettingsAccess)`
+/// (#143). [`SettingsMutation`] is nested inside the club (its members keep
+/// their internal chain). Do NOT add members whose settings read must be
+/// same-frame-exact; order those `.after(SettingsMutation)` instead.
+#[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
+pub struct SettingsAccess;
+
 /// Marker on the root Settings panel entity.
 #[derive(Component, Debug)]
 pub struct SettingsPanel;
@@ -459,7 +472,12 @@ impl Plugin for SettingsPlugin {
                 Update,
                 SettingsMutation
                     .after(crate::layout::LayoutSystem::UpdateOnResize)
-                    .before(crate::game_plugin::GameMutation),
+                    .before(crate::game_plugin::GameMutation)
+                    // Nested in the club: members keep their chain, but
+                    // their pairs against other screen-plugin settings
+                    // accessors are declared irrelevant (#143).
+                    .in_set(SettingsAccess)
+                    .ambiguous_with(SettingsAccess),
             )
             .add_systems(
                 Update,
@@ -482,8 +500,12 @@ impl Plugin for SettingsPlugin {
                     toggle_settings_screen
                         .before(crate::ui_focus::FocusKeys)
                         .ambiguous_with(crate::hud_plugin::HudButtons),
-                    scroll_settings_panel,
-                    crate::ui_modal::touch_scroll_panel::<SettingsPanelScrollable>,
+                    scroll_settings_panel
+                        .in_set(crate::ui_modal::PanelScroll)
+                        .ambiguous_with(crate::ui_modal::PanelScroll),
+                    crate::ui_modal::touch_scroll_panel::<SettingsPanelScrollable>
+                        .in_set(crate::ui_modal::PanelScroll)
+                        .ambiguous_with(crate::ui_modal::PanelScroll),
                 )
                     .chain(),
             );