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

Dockerfile.frontend.prod

@@ -22,12 +22,12 @@ RUN npm install
 
 # Build the application, widget, and webclient. Use the :prod webclient build so
 # the shipped loader bakes the production fallback URL (the real backend URL is
-# resolved at runtime via window.chattermateBaseUrl / APP_CONFIG regardless).
+# resolved at runtime via window.replypierBaseUrl / APP_CONFIG regardless).
 RUN npm run build-only && \
     npm run build:widgetdocker && \
     npm run build:webclient:prod && \
     if [ ! -f dist/index.html ]; then \
-        echo "<!DOCTYPE html><html><head><meta charset='utf-8'><title>ChatterMate</title><link rel='icon' href='/favicon.ico'></head><body><div id='app'></div><script type='module' src='/src/main.ts'></script></body></html>" > dist/index.html; \
+        echo "<!DOCTYPE html><html><head><meta charset='utf-8'><title>ReplyPier</title><link rel='icon' href='/favicon.ico'></head><body><div id='app'></div><script type='module' src='/src/main.ts'></script></body></html>" > dist/index.html; \
     fi
 
 # Production stage