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/app/api/help_center/__init__.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.

backend/app/api/help_center/branding.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.
@@ -75,8 +75,8 @@ def domain_status_response(row: HelpCenterSettings) -> DomainStatusResponse:
             ),
             DnsRecord(
                 type="TXT",
-                host=f"_chattermate.{row.custom_domain}",
-                value=f"cm-verify={row.domain_verification_token}",
+                host=f"_replypier.{row.custom_domain}",
+                value=f"rp-verify={row.domain_verification_token}",
                 verified=row.txt_record_verified,
             ),
         ]
@@ -100,7 +100,7 @@ async def settings_response(
         .all()
     )
     response = HelpCenterSettingsResponse.model_validate(row)
-    # Absolute (api-origin) URL: the admin runs on app.chattermate.chat, whose
+    # Absolute (api-origin) URL: the admin runs on app.replypier.site, whose
     # nginx serves any *.png path as a static asset — a host-relative
     # /api/v1/uploads/*.png would 404 there. Anchor to the backend origin.
     response.logo_url = (

backend/app/api/help_center/domain.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.

backend/app/api/help_center/faqs.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.

backend/app/api/help_center/generation.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.