chore: settle product naming across app, widget and deployments

One word everywhere: ReplyPier in UI copy, package and image names, the
replypier.site domains (app/api/docs/help), REPLYPIER_* settings and the
--rp-* design tokens.

- public widget API is window.ReplyPier with replypierId / replypierBaseUrl /
  replypierConfig / replypierToken, loader at webclient/replypier.min.js;
  both bundles rebuilt from source
- NOTICE, llms.txt, CONTRIBUTING, HELP_CENTER_INFRA and the demo runtime
  config rewritten; the demo config ships no third-party keys
- migration adds the ReplyPier managed model value to the AI model enum
- local compose project, database, role, volume and Docker network carry the
  same name

frontend/scripts/generate-prod-env.ts

@@ -14,9 +14,9 @@ const configContent = `// Runtime configuration - this file gets replaced at con
 // it too; in a page self === window, so window.APP_CONFIG still works.
 self.APP_CONFIG = {
   // API URLs
-  API_URL: "${process.env.VITE_API_URL || 'https://api.chattermate.chat/api/v1'}",
-  WS_URL: "${process.env.VITE_WS_URL || 'wss://api.chattermate.chat'}",
-  WIDGET_URL: "${process.env.VITE_WIDGET_URL || 'https://api.chattermate.chat'}",
+  API_URL: "${process.env.VITE_API_URL || 'https://api.replypier.site/api/v1'}",
+  WS_URL: "${process.env.VITE_WS_URL || 'wss://api.replypier.site'}",
+  WIDGET_URL: "${process.env.VITE_WIDGET_URL || 'https://api.replypier.site'}",
   
   // Firebase Configuration
   FIREBASE_API_KEY: "${process.env.VITE_FIREBASE_API_KEY || ''}",