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/api/test_help_center_tls_ask.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.
@@ -30,7 +30,7 @@ ASK = "/health/help-center-domain"
 
 def test_allows_slug_subdomain():
     # {slug}.HELP_CENTER_BASE_DOMAIN is a help-center host without any DB lookup.
-    assert client.get(ASK, params={"domain": "acme.chattermate.help"}).status_code == 200
+    assert client.get(ASK, params={"domain": "acme.help.replypier.site"}).status_code == 200
 
 
 def test_allows_verified_custom_domain():
@@ -53,4 +53,4 @@ def test_rejects_missing_or_empty_domain():
 def test_normalizes_host_with_port_and_uppercase():
     # SNI can arrive with a port / mixed case; normalize_host must canonicalize
     # it so the slug match still succeeds.
-    assert client.get(ASK, params={"domain": "ACME.chattermate.help:443"}).status_code == 200
+    assert client.get(ASK, params={"domain": "ACME.help.replypier.site:443"}).status_code == 200