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

@@ -25,13 +25,13 @@ uploads/
 *.csr.crt
 /shopify/
 
-# WordPress plugin source lives in its own repo (chattermate-wordpress-plugin);
+# WordPress plugin source lives in its own repo (replypier-wordpress-plugin);
 # only the built, installable zip is tracked here for manual download.
 /wordpress/*
-!/wordpress/chattermate-chat.zip
+!/wordpress/replypier-chat.zip
 
 # Firebase service account key (contains sensitive credentials)
-chattermate-13e0a-firebase-adminsdk-7dqo6-57f3de88cb.json
+*-firebase-adminsdk-*.json
 
 test.db
 *.db
@@ -71,7 +71,7 @@ config/
 frontend/.env.*.bak*
 
 # Stale loader copies — server.js serves the current build from frontend/public/webclient
-chattermate-test/chattermate.min.js
+replypier-test/replypier.min.js
 
 # Only the :dev webclient build emits a sourcemap, and the committed loader is
 # the :prod one, which does not reference it. Keeps a stray dev artifact out.