feat(site): prerender every locale and publish structured data, llms.txt and sitemaps

Crawlers received an empty client-rendered shell (107 characters of text);
most AI crawlers do not run JavaScript, so the product was invisible to them.

- Build renders each locale to static HTML (/ for Korean, /en/ … /vi/) with
  src/entry-server.tsx + scripts/prerender.mjs; the browser hydrates the same
  locale. The language menu links to those pages instead of switching in place.
- Per-locale head: title, description, canonical, hreflang (+ x-default /en/),
  Open Graph and X cards with a per-locale 1200x630 image.
- JSON-LD graph: Organization, WebSite, WebPage, SoftwareApplication (KRW
  offers, version, release date, download URL from the canonical sources),
  HowTo and FAQPage. No invented ratings.
- robots.txt (search, ai-input and ai-train allowed; /app, /api, invites
  excluded), sitemap.xml with language alternates, llms.txt and llms-full.txt
  generated from the same translations and canonical values.
- IndexNow key and a post-deploy ping (Bing, Naver, Yandex).
- A factual "at a glance" section and two FAQ answers (recognised languages,
  where data is stored) in all 10 languages.
- Icons, apple-touch-icon and web manifest; asset base is now absolute so
  sub-path pages load the same bundle.

Verified: 3.6k-7.7k characters of text per page, no hydration warnings,
no overflow at 320/1440 in six locales, axe 0, Lighthouse mobile SEO,
accessibility and best practices 100.

site/src/main.tsx

@@ -1,10 +1,19 @@
 import { StrictMode } from 'react'
-import { createRoot } from 'react-dom/client'
+import { createRoot, hydrateRoot } from 'react-dom/client'
 import { App } from './App'
+import { DEFAULT_LOCALE, isLocale } from './i18n'
 import './index.css'
 
-createRoot(document.getElementById('root')!).render(
+// 빌드 때 언어별로 미리 그린 HTML을 같은 언어로 이어받는다. 언어는 <html lang>이 정본이다.
+const lang = document.documentElement.lang
+const locale = isLocale(lang) ? lang : DEFAULT_LOCALE
+
+const root = document.getElementById('root')!
+const app = (
   <StrictMode>
-    <App />
-  </StrictMode>,
+    <App locale={locale} />
+  </StrictMode>
 )
+// 개발 서버(vite dev)는 미리 그린 HTML 이 없으므로 새로 그린다.
+if (root.firstElementChild) hydrateRoot(root, app)
+else createRoot(root).render(app)