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/api/test_help_center_api.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.
@@ -152,7 +152,7 @@ def test_faq_seo_fields_round_trip(client):
     created = client.post(f"{BASE}/faqs", json={
         "question": "What does it cost?", "answer": "From $19.",
         "slug": "Pricing & Plans!", "meta_title": "Pricing",
-        "meta_description": "What ChatterMate costs.",
+        "meta_description": "What ReplyPier costs.",
     })
     assert created.status_code == 201
     # A hand-typed slug is normalized the same way a generated one is.
@@ -163,7 +163,7 @@ def test_faq_seo_fields_round_trip(client):
     updated = client.put(f"{BASE}/faqs/{faq_id}", json={"slug": "our-pricing"})
     assert updated.json()["slug"] == "our-pricing"
     # Untouched overrides survive a partial update.
-    assert updated.json()["meta_description"] == "What ChatterMate costs."
+    assert updated.json()["meta_description"] == "What ReplyPier costs."
 
 
 def test_faq_slug_is_deduped_but_stable_for_its_own_row(client):