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

deploy/local/compose.yaml

@@ -1,11 +1,11 @@
-name: chattermate-local
+name: replypier-local
 
 services:
   db:
     image: pgvector/pgvector:0.8.2-pg16
     environment:
-      POSTGRES_DB: chattermate
-      POSTGRES_USER: chattermate
+      POSTGRES_DB: replypier
+      POSTGRES_USER: replypier
       POSTGRES_PASSWORD: ${POSTGRES_PASSWORD:?Run ./deploy/local/local.sh init first}
     ports:
       - "127.0.0.1:15432:5432"
@@ -15,7 +15,7 @@ services:
     mem_limit: 384m
     restart: unless-stopped
     healthcheck:
-      test: ["CMD-SHELL", "pg_isready -U chattermate -d chattermate"]
+      test: ["CMD-SHELL", "pg_isready -U replypier -d replypier"]
       interval: 5s
       timeout: 3s
       retries: 20