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/scripts/pingIndexNow.js

@@ -0,0 +1,40 @@
+/**
+ * One IndexNow POST for the URLs in the sitemap. Run after the prod files are published.
+ */
+const fs = require('fs');
+const path = require('path');
+const { INDEXNOW_KEY, indexNowBody, sitemapEntries } = require('./sitemap');
+
+async function pingIndexNow(fetchImpl = fetch, urls) {
+  const keyPath = path.join(__dirname, '..', 'public', `${INDEXNOW_KEY}.txt`);
+  const key = fs.readFileSync(keyPath, 'utf8').trim();
+  if (key !== INDEXNOW_KEY) {
+    throw new Error(`IndexNow key file does not match ${INDEXNOW_KEY}`);
+  }
+  const urlList = urls || sitemapEntries().map((entry) => entry.loc);
+  const body = indexNowBody(key, urlList);
+  const response = await fetchImpl('https://api.indexnow.org/indexnow', {
+    method: 'POST',
+    headers: { 'Content-Type': 'application/json' },
+    body: JSON.stringify(body),
+  });
+  const text = await response.text();
+  if (response.status !== 200 && response.status !== 202) {
+    throw new Error(`IndexNow ${response.status}: ${text}`);
+  }
+  return { status: response.status, body };
+}
+
+async function main() {
+  const result = await pingIndexNow();
+  process.stdout.write(`IndexNow ${result.status}\n`);
+}
+
+module.exports = { pingIndexNow };
+
+if (require.main === module) {
+  main().catch((error) => {
+    process.stderr.write(`${error.message}\n`);
+    process.exit(1);
+  });
+}