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/widget/js-api.spec.ts

@@ -1,7 +1,7 @@
 import { test, expect } from '@e2e'
 
 test.describe('widget JS API', () => {
-  test('the host page opens and closes the chat with window.ChatterMate @widget', async ({ widget }) => {
+  test('the host page opens and closes the chat with window.ReplyPier @widget', async ({ widget }) => {
     await widget.embed()
 
     await widget.api('open')