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/web/app/plugins/antd-style.ts

@@ -0,0 +1,22 @@
+import { createCache, extractStyle } from "ant-design-vue";
+
+/**
+ * Ant Design Vue uses CSS-in-JS. During SSR/SSG we collect the generated styles into a cache
+ * and inline them into <head>, so prerendered HTML is fully styled before hydration (no FOUC).
+ */
+export default defineNuxtPlugin((nuxtApp) => {
+  const cache = createCache();
+
+  if (import.meta.server) {
+    nuxtApp.hook("app:rendered", ({ ssrContext }) => {
+      const css = extractStyle(cache, true);
+      if (css && ssrContext) {
+        ssrContext.head.push({
+          style: [{ key: "antd-cssinjs", innerHTML: css }],
+        });
+      }
+    });
+  }
+
+  return { provide: { antdCache: cache } };
+});

apps/web/app/plugins/api.ts

@@ -0,0 +1,12 @@
+/**
+ * `$api` — $fetch bound to the backend. During SSR it calls the API directly over the internal
+ * network; in the browser it uses the same-origin `/api` path.
+ */
+export default defineNuxtPlugin(() => {
+  const config = useRuntimeConfig();
+  const api = $fetch.create({
+    baseURL: import.meta.server ? config.apiInternalUrl : config.public.apiBase,
+    retry: import.meta.server ? 1 : 0,
+  });
+  return { provide: { api } };
+});