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/input_plugin/mod.rs

@@ -58,6 +58,14 @@ use crate::touch_selection_plugin::TouchSelectionState;
 use crate::ui_theme::{MOTION_DRAG_REJECT_SECS, STATE_SUCCESS, STATE_WARNING};
 use solitaire_core::DrawStockConfig;
 
+/// Set wrapping the core pointer/keyboard input chain (clicks, drags, touch,
+/// hotkeys). Runs between [`crate::game_plugin::PreMutation`] (it reads the
+/// ticked game state) and [`crate::selection_plugin::SelectionKeySet`] (the
+/// selection keys check `DragState::is_idle`); request events it emits are
+/// consumed at `GameMutation` in the same frame (#143).
+#[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
+pub struct PointerInput;
+
 /// System-set labels used to anchor external systems relative to the touch
 /// drag pipeline without duplicating the internal chain ordering.
 #[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
@@ -143,7 +151,13 @@ impl Plugin for InputPlugin {
                     // `.chain()` still orders them relative to each other.
                     handle_keyboard_core
                         .in_set(crate::game_plugin::DrawRequestWriters)
-                        .ambiguous_with(crate::game_plugin::DrawRequestWriters),
+                        .ambiguous_with(crate::game_plugin::DrawRequestWriters)
+                        // N/Z/X/… and U also feed the shared new-game and
+                        // undo request streams (#143).
+                        .in_set(crate::game_plugin::NewGameRequestWriters)
+                        .ambiguous_with(crate::game_plugin::NewGameRequestWriters)
+                        .in_set(crate::game_plugin::UndoRequestWriters)
+                        .ambiguous_with(crate::game_plugin::UndoRequestWriters),
                     handle_keyboard_hint,
                     handle_keyboard_forfeit,
                     handle_stock_click
@@ -159,29 +173,61 @@ impl Plugin for InputPlugin {
                     end_drag.before(GameMutation),
                     // Touch drag pipeline (parallel path through DragState).
                     touch_start_drag.in_set(TouchDragSet::AfterStartDrag),
-                    touch_follow_drag,
+                    // Moves the dragged card's Transform; UiTextFx members
+                    // animate chrome entities only — disjoint domains Bevy
+                    // can't prove (#143).
+                    touch_follow_drag.ambiguous_with(crate::ui_theme::UiTextFx),
                     handle_double_tap, // before touch_end_drag: reads drag state pre-clear
                     touch_end_drag
                         .after(TouchDragSet::BeforeEndDrag)
                         .before(GameMutation),
+                    // Reads StateChangedEvent via cursor — a reset one frame
+                    // after the mutation is invisible (the cycle index only
+                    // matters on the next H press), so it rides at the end
+                    // of the input chain instead of chasing every
+                    // StateChanged writer (#143).
+                    // It also drains the new-game request stream via its own
+                    // cursor, so it joins the writer club the same way
+                    // enqueue_toasts does (#143).
+                    reset_hint_cycle_on_state_change
+                        .in_set(crate::game_plugin::NewGameRequestWriters)
+                        .ambiguous_with(crate::game_plugin::NewGameRequestWriters),
                 )
-                    .chain(),
+                    .chain()
+                    .in_set(PointerInput),
             )
-            .add_systems(Update, reset_hint_cycle_on_state_change);
+            .configure_sets(
+                Update,
+                PointerInput
+                    .after(crate::game_plugin::PreMutation)
+                    .before(crate::selection_plugin::SelectionKeySet)
+                    .before(crate::ui_focus::FocusKeys),
+            );
         // F11 fullscreen toggle is desktop-only; Android windows are always full-screen.
+        // It writes only `Window.mode`; no system reads the mode, and the
+        // geometry change it triggers arrives via WindowResized events on a
+        // later frame — order against Window readers is provably irrelevant
+        // (#143).
         #[cfg(not(target_os = "android"))]
-        app.add_systems(Update, handle_fullscreen);
+        app.add_systems(Update, handle_fullscreen.ambiguous_with_all());
         app
             // Async hint pipeline: state-change drop runs before the
             // poll system so a move applied this frame cancels any
-            // in-flight task before its result can be surfaced.
+            // in-flight task before its result can be surfaced. The poll
+            // emits the hint toast and the pile-highlight event the board
+            // painters consume this frame (#143).
             .add_systems(
                 Update,
                 (
                     crate::pending_hint::drop_pending_hint_on_state_change,
-                    crate::pending_hint::poll_pending_hint_task,
+                    crate::pending_hint::poll_pending_hint_task
+                        .in_set(crate::game_plugin::InfoToastWriters)
+                        .ambiguous_with(crate::game_plugin::InfoToastWriters),
                 )
-                    .chain(),
+                    .chain()
+                    .in_set(crate::pending_hint::PendingHint)
+                    .after(GameMutation)
+                    .before(crate::auto_complete_plugin::AutoComplete),
             );
     }
 }