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/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"):