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/utils/test_agno_utils.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.
@@ -117,21 +117,21 @@ class TestCreateModel:
                 model_name="local-model"
             )
 
-    def test_create_model_chattermate(self):
-        """Test creating CHATTERMATE model (should use OpenAI)"""
+    def test_create_model_replypier(self):
+        """Test creating REPLYPIER model (should use OpenAI)"""
         with patch("app.utils.agno_utils.OpenAIChat") as mock_openai:
             mock_model = MagicMock()
             mock_openai.return_value = mock_model
             
             result = agno_utils.create_model(
-                model_type="CHATTERMATE",
+                model_type="REPLYPIER",
                 api_key="test-api-key",
-                model_name="chattermate-model"
+                model_name="replypier-model"
             )
             
             mock_openai.assert_called_once_with(
                 api_key="test-api-key", 
-                id="chattermate-model", 
+                id="replypier-model", 
                 max_tokens=1000
             )
             assert result == mock_model