fix: manifest-aware layout picker, real carousel items-per-page, hero arrows/swipe/2-panel

Sprint E: homepage section editor now filters the layout-strategy picker
to each widget's widget-manifest.json supportedLayouts instead of always
showing all 5 strategies. columns field gated to widgets that read it
(hero, product-collection carousel).

Sprint F: closes client bug report (no items-per-page control, hero
carousel not manually/automatically scrollable, no 1-2 slide big-carousel
option). Product carousel item width now driven by layout.columns
(reused, was already editable but dead). Hero widget gains prev/next
arrows, touch swipe, and 1-2 panel mode via the same field.

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

src/app/widgets/ui/product-carousel-widget.component.ts

@@ -10,7 +10,7 @@ import { TranslatePipe } from '../../i18n/translate.pipe';
   standalone: true,
   imports: [CommonModule, CatalogProductGridComponent, TranslatePipe],
   template: `
-    <section class="product-carousel-widget">
+    <section class="product-carousel-widget" [style.--items-per-page]="itemsPerPage()">
       @if (data?.title) {
         <h2 class="product-carousel-widget__title">{{ data?.title }}</h2>
       }
@@ -83,7 +83,8 @@ import { TranslatePipe } from '../../i18n/translate.pipe';
 
         ::ng-deep .catalog-product-shell {
           flex: 0 0 auto;
-          width: 220px;
+          width: calc((100% - (var(--items-per-page, 4) - 1) * var(--space-md, 16px)) / var(--items-per-page, 4));
+          min-width: 160px;
         }
       }
 
@@ -121,6 +122,12 @@ export class ProductCarouselWidgetComponent {
     return this.section?.layout?.strategy === 'carousel';
   }
 
+  /** Items visible per page - reuses `layout.columns` (default 4, min 1) rather than a dedicated field. */
+  itemsPerPage(): number {
+    const columns = this.section?.layout?.columns;
+    return columns && columns >= 1 ? Math.floor(columns) : 4;
+  }
+
   scrollBy(direction: -1 | 1): void {
     const el = this.scroller?.nativeElement;
     if (!el) {