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/models/schemas/agent_customization.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.
@@ -60,7 +60,7 @@ class WidgetDisplaySide(str, enum.Enum):
 class WidgetDisplayConfig(BaseModel):
     """Dashboard "Widget placement" defaults, stored in customization_metadata.
 
-    The embed loader (chattermate.js) merges these under any options the
+    The embed loader (replypier.js) merges these under any options the
     installing developer set on the page. Bounds keep saved values renderable
     on any reasonable screen; the loader clamps again client-side.
     """