feat: monorepo with NestJS API, admin panel and DB-driven website

Restructure the repo into a pnpm + Turborepo monorepo:

- apps/web: Nuxt 4 site, now server-rendered and reading all content
  from the API; pages cached with SWR and purged on content changes
- apps/api: NestJS 12 + Prisma 7 + PostgreSQL. Auth with short-lived
  access tokens and rotating httpOnly refresh cookies, roles (ADMIN,
  EDITOR), catalog, editable site sections, media upload to S3-compatible
  storage (converted to WebP), contact messages, audit log
- apps/admin: Vue 3 admin panel (Ant Design Vue, Pinia, Tailwind) for
  products, categories, site sections, messages, media and users
- packages/shared: Zod schemas and types shared by API and admin

Also:
- seed script that loads the original 8 categories / 89 products and
  section content
- Docker images for api (with a one-off migrate service), web, admin,
  and an nginx gateway for both domains
- dev and production compose files, daily database backup service
- API e2e tests

Removes the committed static out/ build and the old root Dockerfile.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

apps/admin/src/utils/format.ts

@@ -0,0 +1,44 @@
+const dateFmt = new Intl.DateTimeFormat("fa-IR-u-ca-persian", {
+  year: "numeric",
+  month: "2-digit",
+  day: "2-digit",
+  hour: "2-digit",
+  minute: "2-digit",
+});
+
+/** ISO date → Jalali date and time, e.g. «۱۴۰۴/۰۷/۲۹، ۱۶:۳۰» */
+export const jalali = (iso: string | null | undefined) => (iso ? dateFmt.format(new Date(iso)) : "—");
+
+export const fileSize = (bytes: number) =>
+  bytes < 1024 * 1024
+    ? `${(bytes / 1024).toLocaleString("fa-IR", { maximumFractionDigits: 0 })} کیلوبایت`
+    : `${(bytes / 1024 / 1024).toLocaleString("fa-IR", { maximumFractionDigits: 1 })} مگابایت`;
+
+export const faNumber = (n: number) => n.toLocaleString("fa-IR");
+
+/** Website base URL for "view on site" links */
+export const SITE_URL = (import.meta.env.VITE_SITE_URL as string | undefined) ?? "http://localhost:3000";
+
+const ACTION_LABELS: Record<string, string> = {
+  create: "ایجاد",
+  update: "ویرایش",
+  delete: "حذف",
+  upload: "آپلود",
+  login: "ورود",
+  publish: "انتشار",
+  unpublish: "عدم انتشار",
+  duplicate: "کپی",
+  reorder: "مرتب‌سازی",
+  "change-password": "تغییر رمز",
+};
+const ENTITY_LABELS: Record<string, string> = {
+  product: "محصول",
+  category: "دسته",
+  section: "بخش سایت",
+  media: "رسانه",
+  user: "کاربر",
+  message: "پیام",
+};
+
+export const activityLabel = (action: string, entity: string) =>
+  `${ACTION_LABELS[action] ?? action} ${ENTITY_LABELS[entity] ?? entity}`;

apps/admin/src/utils/slug.ts

@@ -0,0 +1,7 @@
+/** "Safety Shoes 2" → "safety-shoes-2" (Latin letters and digits only) */
+export const toSlug = (text: string) =>
+  text
+    .toLowerCase()
+    .replace(/[^a-z0-9]+/g, "-")
+    .replace(/^-+|-+$/g, "")
+    .slice(0, 80);