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_public.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.
@@ -34,7 +34,7 @@ from app.models.help_center import HelpCenterSettings
 from app.repositories.faq import FAQRepository
 from app.services.help_center_public import contrast_ink, resolve_help_center, slug_for_host
 
-HOST = "test-org.chattermate.help"
+HOST = "test-org.help.replypier.site"
 
 
 @pytest.fixture(autouse=True)
@@ -108,9 +108,9 @@ def path_client(db, monkeypatch):
 # ---------- helpers ----------
 
 def test_slug_for_host():
-    assert slug_for_host("acme.chattermate.help") == "acme"
-    assert slug_for_host("a.b.chattermate.help") is None
-    assert slug_for_host("chattermate.help") is None
+    assert slug_for_host("acme.help.replypier.site") == "acme"
+    assert slug_for_host("a.b.help.replypier.site") is None
+    assert slug_for_host("help.replypier.site") is None
     assert slug_for_host("help.acme.com") is None
 
 
@@ -279,7 +279,7 @@ def test_widget_embed_points_at_this_install(
     client, db, test_organization, help_center, test_widget, monkeypatch
 ):
     """The loader falls back to the API URL baked in at build time (the vendor
-    cloud) unless the page sets window.chattermateBaseUrl. Without it, a
+    cloud) unless the page sets window.replypierBaseUrl. Without it, a
     self-hosted help center asks the wrong backend for its widget and the
     visitor gets "Chat Unavailable"."""
     monkeypatch.setattr(settings, "BACKEND_URL", "https://api.selfhosted.example")
@@ -287,8 +287,8 @@ def test_widget_embed_points_at_this_install(
     db.commit()
 
     r = client.get("/", headers={"host": HOST})
-    assert f'window.chattermateId = "{test_widget.id}"' in r.text
-    assert 'window.chattermateBaseUrl = "https://api.selfhosted.example/api/v1"' in r.text
+    assert f'window.replypierId = "{test_widget.id}"' in r.text
+    assert 'window.replypierBaseUrl = "https://api.selfhosted.example/api/v1"' in r.text
 
 
 def test_custom_domain_page_is_self_contained(
@@ -316,7 +316,7 @@ def test_custom_domain_page_is_self_contained(
         '<meta property="og:image" content="https://help.customer.com/api/v1/uploads/help_center/logo.png">'
         in r.text
     )
-    assert 'window.chattermateBaseUrl = "https://api.selfhosted.example/api/v1"' in r.text
+    assert 'window.replypierBaseUrl = "https://api.selfhosted.example/api/v1"' in r.text
 
 
 def test_og_card_degrades_without_a_logo(client, db, test_organization, help_center):
@@ -336,7 +336,7 @@ def test_search_filters_results(client, db, test_organization, help_center):
 
 
 def test_disabled_or_unknown_hosts_404(client, db, test_organization, help_center):
-    assert client.get("/", headers={"host": "nope.chattermate.help"}).status_code == 404
+    assert client.get("/", headers={"host": "nope.help.replypier.site"}).status_code == 404
     help_center.enabled = False
     db.commit()
     assert client.get("/", headers={"host": HOST}).status_code == 404
@@ -480,9 +480,9 @@ def test_ask_unanswerable_503(client, db, test_organization, help_center, test_a
 # ---------- host dispatch ----------
 
 def test_is_help_center_host_matches_subdomains_only():
-    assert is_help_center_host("acme.chattermate.help") is True
-    assert is_help_center_host("chattermate.help") is False
-    assert is_help_center_host("api.chattermate.chat") is False
+    assert is_help_center_host("acme.help.replypier.site") is True
+    assert is_help_center_host("help.replypier.site") is False
+    assert is_help_center_host("api.replypier.site") is False
     assert is_help_center_host("") is False
 
 
@@ -566,7 +566,7 @@ def test_preserved_path_drives_canonical_and_json_ld(
 
     r = client.get(MIGRATED_PATH, headers={"host": HOST})
 
-    expected = f"https://test-org.chattermate.help{MIGRATED_PATH}"
+    expected = f"https://test-org.help.replypier.site{MIGRATED_PATH}"
     assert f'<link rel="canonical" href="{expected}">' in r.text
     assert f'<meta property="og:url" content="{expected}">' in r.text
     graph = json.loads(re.search(
@@ -583,7 +583,7 @@ def test_sitemap_lists_the_preserved_path(client, db, test_organization, help_ce
 
     r = client.get("/sitemap.xml", headers={"host": HOST})
 
-    assert f"<loc>https://test-org.chattermate.help{MIGRATED_PATH}</loc>" in r.text
+    assert f"<loc>https://test-org.help.replypier.site{MIGRATED_PATH}</loc>" in r.text
     assert "/a/how-do-i-reset-my-password" not in r.text