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/core/local_file_urls.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.
@@ -34,7 +34,7 @@ LOCAL_FILE_ROUTE = f"{settings.API_V1_STR}/files/local"
 
 # SECRET_KEY also signs JWTs; the purpose prefix keeps the two from ever
 # validating each other.
-_PURPOSE = b"chattermate:local-file-url:v1\n"
+_PURPOSE = b"replypier:local-file-url:v1\n"
 
 
 def _signature(key: str, expires: int) -> str: