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

CONTRIBUTING.md

@@ -1,11 +1,11 @@
-# Contributing to ChatterMate
+# Contributing to ReplyPier
 
 Thanks for your interest in contributing! This document explains how to get
 your changes accepted.
 
 ## License
 
-The ChatterMate open-source core is licensed under the
+The ReplyPier open-source core is licensed under the
 [Apache License 2.0](LICENSE). By contributing, you agree that your
 contributions will be licensed under Apache-2.0.