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/replay_playback.rs

@@ -550,6 +550,14 @@ fn fire_state_changed_on_completion(
     *last_was_completed = now_completed;
 }
 
+/// Set wrapping the replay playback driver chain (tick → auto-clear →
+/// completion `StateChangedEvent`). The tick feeds `MoveRequestEvent` /
+/// `DrawRequestEvent` into this frame's [`GameMutation`], so the set sits
+/// on the pre-mutation spine; the overlay UI (`replay_overlay`) orders
+/// itself after this set so its painters render the post-tick state (#143).
+#[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
+pub struct ReplayPlayback;
+
 /// Bevy plugin that initialises [`ReplayPlaybackState`] and drives
 /// playback ticks, completion linger, and the recording-pause guard.
 ///
@@ -562,18 +570,46 @@ impl Plugin for ReplayPlaybackPlugin {
     fn build(&self, app: &mut App) {
         app.init_resource::<ReplayPlaybackState>()
             .add_message::<StateChangedEvent>()
-            .add_systems(
+            .configure_sets(
                 Update,
-                (
-                    tick_replay_playback,
-                    auto_clear_completed_replay,
-                    fire_state_changed_on_completion,
-                )
-                    .chain(),
+                ReplayPlayback
+                    .after(crate::game_plugin::PreMutation)
+                    // Input first: a stop/pause press or a drag-emitted
+                    // request this frame is observed before the tick fires
+                    // the next scripted move (#143).
+                    .after(crate::input_plugin::PointerInput)
+                    .before(GameMutation),
             )
             .add_systems(
                 Update,
-                record_replay_skip_during_playback.after(GameMutation),
+                (
+                    // The tick shares the move/draw request streams with the
+                    // pointer/keyboard writers (drained wholesale at
+                    // GameMutation) and reads playback speed from settings.
+                    tick_replay_playback
+                        .in_set(crate::game_plugin::MoveRequestWriters)
+                        .ambiguous_with(crate::game_plugin::MoveRequestWriters)
+                        .in_set(crate::game_plugin::DrawRequestWriters)
+                        .ambiguous_with(crate::game_plugin::DrawRequestWriters)
+                        .in_set(crate::settings_plugin::SettingsAccess)
+                        .ambiguous_with(crate::settings_plugin::SettingsAccess),
+                    auto_clear_completed_replay,
+                    // Chained before GameMutation: explicit order against the
+                    // mutation systems' StateChangedEvent writes; readers
+                    // drain the whole queue after GameMutation.
+                    fire_state_changed_on_completion,
+                )
+                    .chain()
+                    .in_set(ReplayPlayback),
+            )
+            .add_systems(
+                Update,
+                record_replay_skip_during_playback
+                    .after(GameMutation)
+                    // After AutoComplete so the stats overlay's watch-replay
+                    // handler (which resets ReplayPlaybackState) and the
+                    // win-path recorder have both settled (#143).
+                    .after(crate::auto_complete_plugin::AutoComplete),
             );
     }
 }