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

backend/app/templates/help_center/base.html

@@ -1,5 +1,5 @@
 {#
-Copyright 2024-2026 ChatterMate
+Copyright 2024-2026 ReplyPier
 
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
@@ -250,8 +250,8 @@ org content safe. Colors: only `--brand`/`--brand-ink` come from the server
     .hc-footer-org .hc-name { font-size: 15px; }
     .hc-powered { display: inline-flex; align-items: center; gap: 8px; text-decoration: none; padding: 7px 13px; border: 1px solid #ececf2; border-radius: 999px; font-size: 12.5px; color: #8a90a0; }
     .hc-powered strong { display: inline-flex; align-items: center; gap: 6px; color: #1a1b25; font-weight: 600; }
-    .hc-cm-mark { width: 15px; height: 15px; border-radius: 5px 5px 5px 1px; background: #c9f24e; display: inline-flex; align-items: center; justify-content: center; gap: 1.5px; }
-    .hc-cm-mark i { width: 2px; height: 2px; border-radius: 50%; background: #0b0c10; }
+    .hc-rp-mark { width: 15px; height: 15px; border-radius: 5px 5px 5px 1px; background: #c9f24e; display: inline-flex; align-items: center; justify-content: center; gap: 1.5px; }
+    .hc-rp-mark i { width: 2px; height: 2px; border-radius: 50%; background: #0b0c10; }
 
     /* progressive enhancement: only hide things once JS takes over */
     .js .hc-tag { display: none; }
@@ -366,9 +366,9 @@ org content safe. Colors: only `--brand`/`--brand-ink` come from the server
         {% endif %}
         <span class="hc-name">{{ row.organization.name }}</span>
       </div>
-      <a class="hc-powered" href="https://chattermate.chat" target="_blank" rel="noopener">
+      <a class="hc-powered" href="https://replypier.site" target="_blank" rel="noopener">
         <span>Powered by</span>
-        <strong><span class="hc-cm-mark"><i></i><i></i><i></i></span> ChatterMate</strong>
+        <strong><span class="hc-rp-mark"><i></i><i></i><i></i></span> ReplyPier</strong>
       </a>
     </div>
   </footer>
@@ -377,19 +377,19 @@ org content safe. Colors: only `--brand`/`--brand-ink` come from the server
   <script type="application/ld+json">{{ json_ld | tojson }}</script>
   {% endif %}
 
-  <!-- open the real embedded ChatterMate widget -->
+  <!-- open the real embedded ReplyPier widget -->
   <script>
   (function () {
-    // The widget script is async and builds its launcher (#chattermate-button)
+    // The widget script is async and builds its launcher (#replypier-button)
     // a moment after load, so a click can land before it exists — poll briefly
     // and click as soon as it appears instead of silently doing nothing.
     function openChat() {
       var tries = 0;
       (function attempt() {
-        var btn = document.getElementById('chattermate-button');
+        var btn = document.getElementById('replypier-button');
         if (btn) { btn.click(); return; }
         if (tries++ < 40) { setTimeout(attempt, 150); return; }  // ~6s
-        if (window.console) console.warn('[ChatterMate] chat widget is not available on this page.');
+        if (window.console) console.warn('[ReplyPier] chat widget is not available on this page.');
       })();
     }
     [].slice.call(document.querySelectorAll('[data-chat]')).forEach(function (b) {
@@ -402,12 +402,12 @@ org content safe. Colors: only `--brand`/`--brand-ink` come from the server
 
   {% if widget_id %}
   <script>
-    window.chattermateId = {{ widget_id | tojson }};
+    window.replypierId = {{ widget_id | tojson }};
     // Must be set, exactly like the dashboard's install snippet does: the loader
     // otherwise falls back to the API URL baked in at build time (the vendor
     // cloud), so a self-hosted help center would ask the wrong backend for its
     // widget and the visitor would just see "Chat Unavailable".
-    window.chattermateBaseUrl = {{ widget_api_url | tojson }};
+    window.replypierBaseUrl = {{ widget_api_url | tojson }};
     (function () {
       var s = document.createElement('script');
       s.src = {{ widget_script_url | tojson }};