fix(engine): Restore-prompt resolution suppresses Home auto-show

Resolving the Welcome-back / Restore prompt (either Continue or New
game) cleared `PendingRestoredGame` and despawned the modal, but the
launch-time Home auto-show then fired the next frame and stacked
itself over the player's chosen path — clicking "New game" would deal
a fresh game AND immediately pop the mode picker on top.

`LaunchHomeShown` becomes pub so `handle_restore_prompt` can flip it
to `true` after either resolution; `M` still re-opens the picker on
demand. Headless tests already pre-set the flag to true via
`HomePlugin::headless()`, so they're unaffected.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

solitaire_engine/src/home_plugin.rs

@@ -120,8 +120,12 @@ struct HomeModeCard(HomeMode);
 /// the first time it spawns the modal, so the auto-show is one-shot per
 /// process — subsequent dismissals (Cancel / mode pick) don't trigger
 /// a respawn, but the player can still re-open the picker with `M`.
+///
+/// Other plugins (e.g. `game_plugin`'s restore-prompt handler) can flip
+/// the flag manually to suppress the launch auto-show when the player
+/// has already made a launch-time choice through a different surface.
 #[derive(Resource, Debug, Default)]
-struct LaunchHomeShown(bool);
+pub struct LaunchHomeShown(pub bool);
 
 // ---------------------------------------------------------------------------
 // Plugin