Persist last selected category across menu restarts

- Track the most recently chosen category in module scope so it survives scene.start() reusing the same instance.
- Fall back to that value when entering the menu without explicit category data, restoring the user's previous selection instead of defaulting.

src/scenes/GameMenuScene.js

@@ -24,12 +24,19 @@ const ICON_X_OFFSET = -145;
 // How far (px) a grid travels off screen when switching categories.
 const GRID_TRAVEL = GAME_WIDTH + 800;
 
+// The most recently selected category. Module scope so it survives scene
+// restarts (scene.start() reuses the instance) and also covers paths that
+// start the menu without category data — the menu always returns to where
+// the user last was.
+let lastCategory = null;
+
 export default class GameMenuScene extends Phaser.Scene {
   constructor() { super('GameMenu'); }
 
   init(data) {
-    // Set when coming back from the opponent picker — restore that category.
-    this._initialCategory = (data && data.category) || null;
+    // Category to restore on entry: the explicit one (coming back from the
+    // opponent picker) or the most recently selected one.
+    this._initialCategory = (data && data.category) || lastCategory;
     // scene.start() reuses the existing scene instance, so instance props from
     // the previous visit survive — reset them so this create() starts clean
     // (otherwise showCategory()'s "same category" guard swallows the restore).
@@ -152,6 +159,7 @@ export default class GameMenuScene extends Phaser.Scene {
   showCategory(key) {
     if (key === this._currentCategory) return;
     this._currentCategory = key;
+    lastCategory = key;
 
     if (this._hintText) { this._hintText.destroy(); this._hintText = null; }
     if (this._titleText) {