Add a public homepage so visitors can tell what Hesychia is.

Logged-out / is the marketing site. Signed-in / still opens chat.
Closes #113, #114, #115, and #116.

Co-authored-by: Cursor <cursoragent@cursor.com>

llm-fe/public/robots.txt

@@ -1,3 +1,16 @@
 # https://www.robotstxt.org/robotstxt.html
 User-agent: *
-Disallow:
+Allow: /
+Disallow: /signin/
+Disallow: /signup/
+Disallow: /account/
+Disallow: /document_storage
+Disallow: /feedback/
+Disallow: /analytics/
+Disallow: /password_reset/
+Disallow: /password_reset_confirmation/
+Disallow: /set_password/
+Disallow: /auth/
+Disallow: /billing/
+
+Sitemap: https://hesychia.ai/sitemap.xml