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/main.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.
@@ -83,7 +83,7 @@ logger.debug(f"CORS origins: {cors_origins}")
 app.router.lifespan_context = lifespan
 
 # Add CORS middleware to FastAPI app. The regex covers every help-center
-# subdomain (*.chattermate.help) so a newly-created slug is allowed without a
+# subdomain (*.help.replypier.site) so a newly-created slug is allowed without a
 # cache refresh; explicit origins still cover org domains + custom domains.
 # Only first-party origins (the dashboard) may send credentials.
 app.add_middleware(
@@ -319,7 +319,7 @@ async def root():
     return {
         "name": settings.PROJECT_NAME,
         "version": settings.VERSION,
-        "description": "Welcome to ChatterMate API"
+        "description": "Welcome to ReplyPier API"
     }
 
 @app.api_route("/health", methods=["GET"], operation_id="get_health_check")