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

e2e/specs/perf/budgets.spec.ts

@@ -6,7 +6,7 @@ import { test, expect, env, AI_REPLY } from '@e2e'
 
 const KB = 1024
 const BUDGETS = [
-  { file: 'embed loader (chattermate.min.js)', url: `${env.frontendUrl}/webclient/chattermate.min.js`, maxBytes: 60 * KB },
+  { file: 'embed loader (replypier.min.js)', url: `${env.frontendUrl}/webclient/replypier.min.js`, maxBytes: 60 * KB },
   { file: 'widget script (widget.js)', url: `${env.backendUrl}/assets/widget.js`, maxBytes: 500 * KB },
   { file: 'widget styles (widget.css)', url: `${env.backendUrl}/assets/widget.css`, maxBytes: 135 * KB },
 ]