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/tests/services/test_faq_article_import.py

@@ -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.
@@ -165,7 +165,7 @@ def test_fetch_article_converts_markdown_strips_chrome_and_collects_images():
     # Link absolutized (same-site remapping happens later, in the import job).
     assert "[pricing](https://help.example.com/pricing)" in article.markdown
     # Real image collected as placeholder; data: image reduced to alt text.
-    assert "cm-pending-image://0.img" in article.markdown
+    assert "rp-pending-image://0.img" in article.markdown
     assert len(article.pending_images) == 1
     assert "base64" not in article.markdown
     # Help-center chrome stripped: no Chatwoot footer, breadcrumb or metadata.