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/vite.config.ts

@@ -87,9 +87,9 @@ export default defineConfig(({ command, mode }) => {
       // script stays the first script tag and embedded contexts never register.
       injectRegister: false,
       manifest: {
-        name: 'ChatterMate',
-        short_name: 'ChatterMate',
-        description: 'Agent console for ChatterMate — handle customer chats anywhere.',
+        name: 'ReplyPier',
+        short_name: 'ReplyPier',
+        description: 'Agent console for ReplyPier — handle customer chats anywhere.',
         start_url: '/',
         scope: '/',
         display: 'standalone',
@@ -127,7 +127,7 @@ export default defineConfig(({ command, mode }) => {
       '.ngrok.app',
       '.ngrok.io',
       'frontendchat.ngrok.app',
-      '.chattermate.chat',
+      '.replypier.site',
     ],
   },
   publicDir: 'public',