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/alembic/versions/f7a1c2d3e4b5_add_faq_help_center.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.
@@ -21,7 +21,7 @@ Revises: drop_slack_tables_001
 Create Date: 2026-07-12
 
 New feature: AI-generated FAQs reviewed/published by the org and served as a
-public help center on {slug}.chattermate.help or a verified custom domain.
+public help center on {slug}.help.replypier.site or a verified custom domain.
 
 Tables:
 - faq_generation_jobs: async generate/import jobs (worker + UI polling)