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/pending_hint.rs

@@ -39,6 +39,13 @@ use crate::resources::{GameStateResource, HintCycleIndex};
 /// emits the hint visuals once the task completes. At most one task
 /// is ever in flight: a fresh H press while a previous task is
 /// running drops the previous task and queues the new one.
+/// Set wrapping the async hint pipeline (state-change drop → poll). The
+/// HUD hint button orders `.before` it so a press cancels/spawns before
+/// this frame's poll; the drag-highlight painters order `.after` it so
+/// the hint sprite writes are settled (#143).
+#[derive(bevy::ecs::schedule::SystemSet, Debug, Clone, PartialEq, Eq, Hash)]
+pub struct PendingHint;
+
 #[derive(Resource, Default)]
 pub struct PendingHintTask {
     /// `Some` while the solver is still working on a verdict.