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

backend/.env.example

@@ -1,5 +1,5 @@
 # Database Configuration
-DATABASE_URL=postgresql+psycopg://postgres:postgres@db:5432/chattermate
+DATABASE_URL=postgresql+psycopg://postgres:postgres@db:5432/replypier
 
 # CORS Configuration add backend url to allow cors from frontend
 CORS_ORIGINS=["http://localhost:3000","http://localhost:8000"]
@@ -61,7 +61,7 @@ ENVIRONMENT=development
 
 # S3 Configuration
 S3_FILE_STORAGE=false
-S3_BUCKET=chattermate-uploads
+S3_BUCKET=replypier-uploads
 S3_REGION=us-east-1
 # Leave both blank on EC2/ECS/EKS to use the attached IAM role — boto3 then
 # resolves credentials from its default chain. Set them only for static keys;