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/knowledge/test_enhanced_website_reader.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.
@@ -155,7 +155,7 @@ class TestEnhancedWebsiteReader(unittest.TestCase):
     def test_the_page_title_survives_when_it_sits_in_a_page_header(self):
         """Docs themes put the <h1> in a <header>, which selection treats as chrome.
 
-        docs.chattermate.chat lost "Quickstart: Launch Your AI Support Agent in
+        docs.replypier.site lost "Quickstart: Launch Your AI Support Agent in
         5 Minutes" that way. A page's title is its strongest retrieval signal,
         so losing it makes the page harder for an agent to find, not just
         shorter.