Public page SEO and production analytics (#125)

## Summary
- Closes the public-page gaps from #124: each route gets its own title, description, canonical, heading, links, and JSON-LD, and unknown URLs have a real 404 document.
- Adds HeyCatch and the Google tag (`G-V12DLRLPWR`) only on the production site and the iOS and Android apps. Tianji still loads on beta.
- Needs the server-infra change that stops serving the app shell for missing paths.

## Test plan
- [ ] Build production and confirm `/` and `/pricing/` HTML include a unique title, description, canonical, one h1, social tags, related links, and Organization JSON-LD.
- [ ] Confirm a nonsense path is served as `404.html` once the nginx change is deployed.
- [ ] Confirm beta and local web do not load HeyCatch or gtag, and that a production or native build does.
- [ ] Open the live site after deploy and click around, then mark HeyCatch installed in its dashboard.

Reviewed-on: #125

llm-fe/public/sitemap.xml

@@ -2,19 +2,19 @@
 <urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
   <url>
     <loc>https://hesychia.ai/</loc>
-    <lastmod>2026-10-17</lastmod>
+    <lastmod>2026-10-19</lastmod>
   </url>
   <url>
     <loc>https://hesychia.ai/pricing/</loc>
-    <lastmod>2026-10-17</lastmod>
+    <lastmod>2026-10-19</lastmod>
   </url>
   <url>
     <loc>https://hesychia.ai/privacy/</loc>
-    <lastmod>2026-10-17</lastmod>
+    <lastmod>2026-10-19</lastmod>
   </url>
   <url>
     <loc>https://hesychia.ai/changelog/</loc>
-    <lastmod>2026-10-17</lastmod>
+    <lastmod>2026-08-04</lastmod>
   </url>
   <url>
     <loc>https://hesychia.ai/terms_of_service/</loc>