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/api/tsconfig.json

@@ -0,0 +1,24 @@
+{
+  "compilerOptions": {
+    "module": "nodenext",
+    "moduleResolution": "nodenext",
+    "resolvePackageJsonExports": true,
+    "esModuleInterop": true,
+    "isolatedModules": true,
+    "declaration": false,
+    "removeComments": true,
+    "emitDecoratorMetadata": true,
+    "experimentalDecorators": true,
+    "allowSyntheticDefaultImports": true,
+    "target": "ES2023",
+    "sourceMap": true,
+    "outDir": "./dist",
+    "rootDir": ".",
+    "incremental": true,
+    "skipLibCheck": true,
+    "strict": true,
+    "strictPropertyInitialization": false,
+    "types": ["node", "multer", "vitest/globals"]
+  },
+  "include": ["src", "test", "prisma", "prisma.config.ts", "vitest.config.e2e.ts"]
+}