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/play_by_seed_plugin.rs

@@ -115,10 +115,27 @@ impl Plugin for PlayBySeedPlugin {
                 Update,
                 (
                     handle_open_dialog,
-                    handle_text_input,
-                    tick_debounce_and_spawn_solver_task,
-                    poll_solver_task,
-                    handle_confirm,
+                    // Writes the marker-filtered seed-dialog Text nodes —
+                    // disjoint from the other text painters (UiTextFx
+                    // club, #143).
+                    handle_text_input
+                        .in_set(crate::ui_theme::UiTextFx)
+                        .ambiguous_with(crate::ui_theme::UiTextFx),
+                    tick_debounce_and_spawn_solver_task
+                        .in_set(crate::ui_theme::UiTextFx)
+                        .ambiguous_with(crate::ui_theme::UiTextFx)
+                        // Reads deal settings for the solver spawn; a frame
+                        // of lag is invisible (#143).
+                        .in_set(crate::settings_plugin::SettingsAccess)
+                        .ambiguous_with(crate::settings_plugin::SettingsAccess),
+                    poll_solver_task
+                        .in_set(crate::ui_theme::UiTextFx)
+                        .ambiguous_with(crate::ui_theme::UiTextFx),
+                    // Shares the new-game request stream with the other
+                    // writers (drained wholesale at GameMutation, #143).
+                    handle_confirm
+                        .in_set(crate::game_plugin::NewGameRequestWriters)
+                        .ambiguous_with(crate::game_plugin::NewGameRequestWriters),
                     handle_cancel,
                 )
                     .chain()