fix(engine): platform-correct onboarding copy; Home waits for first-run onboarding (Phase H)

- The how-to-play slide told touch players to left/right-click; Android
  now gets tap/double-tap copy pointing at the bottom-bar Hint button.
- On a fresh profile the Home auto-show spawned underneath the
  onboarding modal, stacking two scrims (v0.44.0 emulator smoke
  finding). spawn_home_on_launch now waits until first_run_complete
  and the onboarding modal is gone, so the launch beat is onboarding,
  then Home, then the table.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

solitaire_engine/src/home_plugin.rs

@@ -475,6 +475,11 @@ fn persist_last_mode(
 ///   must be empty — when the player has a saved in-progress game the
 ///   restore prompt takes precedence; the home picker would compete
 ///   with it for attention.
+/// * First-run onboarding must be finished (`Settings.first_run_complete`
+///   and no `OnboardingScreen` open) — on a fresh profile the onboarding
+///   owns the launch beat; Home appearing underneath it stacked two
+///   modals (Phase H fix; spotted in the v0.44.0 emulator smoke). Home
+///   spawns on the first frame after the player finishes or skips.
 /// * `HomeScreen` must not already exist (defensive — e.g. the player
 ///   pressed `M` between ticks).
 /// * `LaunchHomeShown` flips to `true` after the first spawn so this
@@ -488,6 +493,7 @@ fn spawn_home_on_launch(
     splash: Query<(), With<crate::splash_plugin::SplashRoot>>,
     restore_prompts: Query<(), With<crate::game_plugin::RestorePromptScreen>>,
     pending_restore: Option<Res<crate::game_plugin::PendingRestoredGame>>,
+    onboarding: Query<(), With<crate::onboarding_plugin::OnboardingScreen>>,
     existing: Query<(), With<HomeScreen>>,
     sources: HomeSpawnSources,
     mut deal_expanded: ResMut<DealOptionsExpanded>,
@@ -496,6 +502,11 @@ fn spawn_home_on_launch(
         || !splash.is_empty()
         || !restore_prompts.is_empty()
         || pending_restore.as_ref().is_some_and(|p| p.0.is_some())
+        || !onboarding.is_empty()
+        || sources
+            .settings
+            .as_ref()
+            .is_some_and(|s| !s.0.first_run_complete)
         || !existing.is_empty()
     {
         return;