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/tests/services/test_channel_status.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.
@@ -308,7 +308,7 @@ async def test_failed_after_read_changes_nothing(db, account, test_organization,
 @pytest.mark.asyncio
 async def test_every_receipt_is_announced_even_for_unknown_messages(
         db, account, use_test_db, mock_sio, redis):
-    """Usage counting needs receipts for messages ChatterMate never stored."""
+    """Usage counting needs receipts for messages ReplyPier never stored."""
     seen = []
 
     async def listen(event):