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/tsconfig.node.json

@@ -0,0 +1,14 @@
+{
+  "compilerOptions": {
+    "tsBuildInfoFile": "./node_modules/.tmp/tsconfig.node.tsbuildinfo",
+    "target": "ES2023",
+    "lib": ["ES2023"],
+    "module": "ESNext",
+    "moduleResolution": "bundler",
+    "types": ["node"],
+    "strict": true,
+    "skipLibCheck": true,
+    "noEmit": true
+  },
+  "include": ["vite.config.ts"]
+}