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

deploy/local/demo.template.html

@@ -37,10 +37,10 @@
     <p class="note">套餐、政策与校验码均为虚构测试数据。此页面仅供本机测试；对话会调用已配置的模型 API。</p>
   </main>
   <script>
-    window.chattermateId = "__WIDGET_ID__";
-    window.chattermateBaseUrl = "http://127.0.0.1:8018/api/v1";
-    window.chattermateConfig = { position: "bottom-right" };
+    window.replypierId = "__WIDGET_ID__";
+    window.replypierBaseUrl = "http://127.0.0.1:8018/api/v1";
+    window.replypierConfig = { position: "bottom-right" };
   </script>
-  <script src="/webclient/chattermate.min.js"></script>
+  <script src="/webclient/replypier.min.js"></script>
 </body>
 </html>