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

AGENT_HANDOFF.md

@@ -30,7 +30,7 @@
 | PostgreSQL 16 + pgvector | `127.0.0.1:15432` |
 | Redis | `127.0.0.1:16380` |
 
-Docker context 为 `colima-bytedesk`，Compose 项目名为 `chattermate-local`，数据库卷为 `chattermate-local_postgres_data`。它们是运行配置，不能为整理名称而改动或删除。Colima 虚拟机承载数据库与缓存，不要单独关闭。
+Docker context 为 `colima-bytedesk`，Compose 项目名为 `replypier-local`，数据库卷为 `replypier-local_postgres_data`。它们是运行配置，不能为整理名称而改动或删除。Colima 虚拟机承载数据库与缓存，不要单独关闭。
 
 ## 配置与数据保护