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/package-lock.json

@@ -1,10 +1,10 @@
 {
-  "name": "chattermate-e2e",
+  "name": "replypier-e2e",
   "lockfileVersion": 3,
   "requires": true,
   "packages": {
     "": {
-      "name": "chattermate-e2e",
+      "name": "replypier-e2e",
       "devDependencies": {
         "@axe-core/playwright": "4.13.0",
         "@modelcontextprotocol/sdk": "1.30.1",