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

HELP_CENTER_INFRA.md

@@ -6,11 +6,10 @@ deploy-time pieces that live **outside** the repo: DNS, TLS and the host
 nginx on the production VPS. `frontend/nginx.conf` and the docker-compose
 files need **no changes**.
 
-> **As deployed on the ReplyPier cloud VPS (2026-07-14):** the base domain is
-> **`help.replypier.site`** (orgs serve at `{slug}.help.replypier.site`), not
-> the `help.replypier.site` this doc originally planned — that domain was never
-> registered, and the org only owns `replypier.site`. DNS is **Route53**, so the
-> wildcard cert is issued and auto-renewed with the `dns-route53` plugin.
+> **As deployed on the ReplyPier VPS (2026-07-14):** the base domain is
+> **`help.replypier.site`** (orgs serve at `{slug}.help.replypier.site`). DNS is
+> **Route53**, so the wildcard cert is issued and auto-renewed with the
+> `dns-route53` plugin.
 > Placeholders (`<VPS_IPV4>`, `<ZONE_ID>`, …) stand in for the live values; the
 > real ones live on the VPS and in ops notes, not in this public repo.