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

replypier-test/package.json

@@ -0,0 +1,12 @@
+{
+  "name": "replypier-test",
+  "version": "1.0.0",
+  "type": "module",
+  "scripts": {
+    "start": "node server.js"
+  },
+  "dependencies": {
+    "cors": "^2.8.5",
+    "express": "^5.2.1"
+  }
+}