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

.gitignore

@@ -31,7 +31,7 @@ uploads/
 !/wordpress/replypier-chat.zip
 
 # Firebase service account key (contains sensitive credentials)
-replypier-13e0a-firebase-adminsdk-7dqo6-57f3de88cb.json
+*-firebase-adminsdk-*.json
 
 test.db
 *.db