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/vite.widget.docker.config.ts

@@ -16,7 +16,7 @@ export default defineConfig({
   build: {
     lib: {
       entry: resolve(__dirname, 'src/webclient/widget.ts'),
-      name: 'ChatterMateWidget',
+      name: 'ReplyPierWidget',
       fileName: 'widget',
       formats: ['es'],
     },