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/services/test_domain_verification.py

@@ -151,7 +151,7 @@ def test_domain_endpoints_flow(client, db, test_organization):
     assert body["custom_domain"] == "help.customer.com"
     assert body["domain_status"] == "pending"
     assert [r["type"] for r in body["records"]] == ["CNAME", "TXT"]
-    assert body["records"][1]["host"] == "_replypier.customer.com"
+    assert body["records"][1]["host"] == "_replypier.help.customer.com"
 
     with patch.object(dv, "check_txt_record", return_value=True), \
          patch.object(dv, "check_cname_record", return_value=True), \

backend/tests/services/test_sql_guardrails.py

@@ -359,7 +359,7 @@ class TestRowScopeCaseInsensitivity:
         )
 
     def test_predicate_folds_both_sides(self):
-        result = self._ci("Arun@replypier.site")
+        result = self._ci("Arun@ReplyPier.Site")
         assert result.ok
         assert "LOWER(customer_email) = '%s'" % OWNER in result.sql
 
@@ -369,10 +369,10 @@ class TestRowScopeCaseInsensitivity:
         assert "'x'' or ''1''=''1'" in result.sql.lower()
 
     def test_exact_match_when_disabled(self):
-        result = scoped("SELECT id FROM orders", value="Arun@replypier.site")
+        result = scoped("SELECT id FROM orders", value="Arun@ReplyPier.Site")
         assert result.ok
         assert "LOWER(" not in result.sql
-        assert "customer_email = 'Arun@replypier.site'" in result.sql
+        assert "customer_email = 'Arun@ReplyPier.Site'" in result.sql
 
     def test_still_fails_closed(self):
         result = self._ci(value=None)

backend/tests/services/test_ticket_privacy.py

@@ -41,7 +41,7 @@ class TestScrubOutbound:
         assert scrub_outbound(text, (OWNER_EMAIL,)) == text
 
     def test_own_email_matched_case_insensitively(self):
-        text = "Your account Arun@replypier.site is fixed."
+        text = "Your account Arun@ReplyPier.Site is fixed."
         assert scrub_outbound(text, (OWNER_EMAIL,)) == text
 
     def test_own_phone_survives_reformatting(self):

backend/tests/tools/test_ticket_toolkit.py

@@ -34,7 +34,7 @@ from app.tools.ticket_toolkit import TicketTools, _clean_email, _clean_name
 
 class TestCleanEmail:
     def test_normalizes_and_lowercases(self):
-        assert _clean_email("  Admin@replypier.site ") == "admin@replypier.site"
+        assert _clean_email("  Admin@ReplyPier.Site ") == "admin@replypier.site"
 
     def test_rejects_junk(self):
         for bad in (None, "", "not-an-email", "no@domain", "@no-local.com", "a b@c.com"):