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_offtopic_exercise.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.
@@ -68,7 +68,7 @@ class TestCatchesTheAbuse:
         assert detect_offtopic_exercise(PROD_BRIEF) is True
 
     def test_still_caught_when_org_name_is_known(self):
-        assert detect_offtopic_exercise(PROD_BRIEF, ["ChatterMate"]) is True
+        assert detect_offtopic_exercise(PROD_BRIEF, ["ReplyPier"]) is True
 
 
 class TestPrecision:
@@ -121,5 +121,5 @@ class TestThresholds:
         assert detect_offtopic_exercise(text) is False
 
     def test_org_name_mention_anchors_it(self):
-        text = PROD_BRIEF + "\nWe need this for our ChatterMate integration."
-        assert detect_offtopic_exercise(text, ["ChatterMate"]) is False
+        text = PROD_BRIEF + "\nWe need this for our ReplyPier integration."
+        assert detect_offtopic_exercise(text, ["ReplyPier"]) is False