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/knowledge/test_crawler_identity.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.
@@ -26,7 +26,7 @@ from app.knowledge.failure_advice import FAILURE_ADVICE, FailureCause, plain_rea
 
 
 def test_identifies_honestly_by_name():
-    assert "ChatterMateBot" in CRAWLER_USER_AGENT
+    assert "ReplyPierBot" in CRAWLER_USER_AGENT
     assert "Chrome/" not in CRAWLER_USER_AGENT  # the stale fake that WordPress.com refuses
 
 
@@ -43,7 +43,7 @@ def test_browser_fallback_uses_the_shared_identity():
 
 
 def test_a_refusal_reads_as_a_refusal():
-    url = "https://chattermate.chat"
+    url = "https://replypier.site"
     reason = plain_reason(FAILURE_ADVICE[FailureCause.BOT_BLOCKED].format(url=url), url)
     assert reason.startswith("This site refused our crawler.")
     assert "challenge page" not in reason