refactor: move filter bar to GameList and fix button styling

- Moved filter button bar from App.jsx to GameList.jsx for better separation of concerns.
- Updated GameList to accept filter/setFilter props and render the filter bar internally.
- Moved .new-game-button styles to global CSS for consistent styling.
- Ensured filter button styles remain in GameList.module.css.
- Improves modularity and UI consistency.

src/styles/index.css

@@ -56,4 +56,24 @@ input, select {
         width: 40px;
         height: 40px;
     }
+}
+
+.new-game-button {
+  width: 100%;
+  background: #222;
+  color: #fff;
+  border: none;
+  border-radius: 0;
+  font-size: 1.4rem;
+  font-weight: 600;
+  padding: 20px 0;
+  margin-bottom: 16px;
+  cursor: pointer;
+  transition: background 0.2s, color 0.2s;
+  text-align: center;
+  display: block;
+}
+
+.new-game-button:hover {
+  background: #333;
 }