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

deploy/server/config.example.json

@@ -9,7 +9,7 @@
   "known_hosts": "/etc/replypier-updater/known_hosts",
   "owner_ids": ["REPLACE_WITH_DEPLOYMENT_OWNER_USER_ID"],
   "initial_revision": "REPLACE_WITH_INSTALLED_COMMIT",
-  "db_container": "chattermate-local-db-1",
-  "db_user": "chattermate",
-  "db_name": "chattermate"
+  "db_container": "replypier-local-db-1",
+  "db_user": "replypier",
+  "db_name": "replypier"
 }