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

frontend/nginx.conf

@@ -11,7 +11,7 @@ server {
 
     # Enhanced Security headers.
     # This config only ever runs inside the frontend image, i.e. for self-hosted
-    # deployments - app.chattermate.chat serves the SPA from its own reverse proxy
+    # deployments - app.replypier.site serves the SPA from its own reverse proxy
     # and never routes here, so its CSP is set there and is unaffected by this file.
     # The CSP is repeated in every location block below because an add_header inside
     # a location cancels the inherited ones - change one, change all five.