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/game_plugin/mod.rs

@@ -99,6 +99,38 @@ pub struct DrawRequestWriters;
 #[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
 pub struct InfoToastWriters;
 
+/// Self-ambiguous club for writers of `MoveRequestEvent` (drag drops, stock
+/// clicks, radial menu, selection keys, replay step button). Consumers drain
+/// the whole queue — append order is meaningless (#143). Same rules as
+/// [`NewGameRequestWriters`]: do NOT hang ordering edges off this set.
+#[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
+pub struct MoveRequestWriters;
+
+/// Self-ambiguous club for writers of `WarningToastEvent` (daily-expiry
+/// warning, leaderboard opt-in/out failure polls). The toast pipeline
+/// drains the whole queue — append order is meaningless (#143). Same
+/// rules as [`InfoToastWriters`].
+#[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
+pub struct WarningToastWriters;
+
+/// Set + self-ambiguous club for the mode-start request handlers (challenge,
+/// daily, time-attack, play-by-seed, difficulty). Each drains its own
+/// request stream and resets `GameStateResource` for its mode; only one
+/// stream carries an event on any real frame, so member order is irrelevant
+/// (club), while the set as a whole runs between the stats abandon-recorder
+/// ([`crate::stats_plugin::AbandonRecord`], which must read the old game
+/// first) and [`GameMutation`] (#143).
+#[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
+pub struct ModeStart;
+
+/// Set wrapping `GamePlugin`'s pre-mutation game-state spine (elapsed-time
+/// tick, settings sync, restore prompt). Sits between
+/// [`crate::settings_plugin::SettingsMutation`] and [`GameMutation`]; other
+/// pre-mutation readers of `GameStateResource` (e.g. the stats
+/// abandon-recorder) order themselves `.after(PreMutation)` (#143).
+#[derive(SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
+pub struct PreMutation;
+
 /// Persistence path for the in-progress game state file. `None` disables I/O.
 #[derive(Resource, Debug, Clone)]
 pub struct GameStatePath(pub Option<PathBuf>);
@@ -267,7 +299,14 @@ impl Plugin for GamePlugin {
                     .in_set(InfoToastWriters)
                     .ambiguous_with(InfoToastWriters),
             )
-            .add_systems(Update, record_replay_on_win.after(GameMutation))
+            .add_systems(
+                Update,
+                record_replay_on_win
+                    .after(GameMutation)
+                    // Before the playback skip-recorder (which runs after
+                    // AutoComplete) — both touch RecordingReplay (#143).
+                    .before(crate::auto_complete_plugin::AutoComplete),
+            )
             .add_systems(
                 Update,
                 (
@@ -301,9 +340,20 @@ impl Plugin for GamePlugin {
                         .ambiguous_with(NewGameRequestWriters),
                 )
                     .chain()
+                    .in_set(PreMutation),
+            )
+            .configure_sets(
+                Update,
+                PreMutation
                     .after(crate::settings_plugin::SettingsMutation)
                     .before(GameMutation),
             )
+            .configure_sets(
+                Update,
+                ModeStart
+                    .after(crate::stats_plugin::AbandonRecord)
+                    .before(GameMutation),
+            )
             .init_resource::<AutoSaveTimer>()
             .add_systems(Update, auto_save_game_state.after(GameMutation))
             .add_systems(Last, save_game_state_on_exit);