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/local.sh

@@ -60,10 +60,10 @@ build_frontend() {
   if [[ ! -f "${STATE}/assets/widget.css" ]]; then
     cp "${STATE}"/assets/unused/*.css "${STATE}/assets/widget.css"
   fi
-  node_modules/.bin/esbuild src/webclient/chattermate.js --bundle --minify --format=iife \
+  node_modules/.bin/esbuild src/webclient/replypier.js --bundle --minify --format=iife \
     --target=es2015 --loader:.svg=text --define:process.env.NODE_ENV='"production"' \
-    --define:__CHATTERMATE_API_URL__='"http://127.0.0.1:8018/api/v1"' \
-    --outfile="${STATE}/dashboard/webclient/chattermate.min.js"
+    --define:__REPLYPIER_API_URL__='"http://127.0.0.1:8018/api/v1"' \
+    --outfile="${STATE}/dashboard/webclient/replypier.min.js"
   cat > "${STATE}/dashboard/config.js" <<'JS'
 self.APP_CONFIG = {
   API_URL: "http://127.0.0.1:8018/api/v1",
@@ -112,7 +112,7 @@ case "${1:-status}" in
       colima --profile bytedesk start --activate=false --ssh-config=false
     fi
     compose up -d --wait --wait-timeout 180
-    compose exec -T db psql -U chattermate -d chattermate -c 'CREATE EXTENSION IF NOT EXISTS vector;'
+    compose exec -T db psql -U replypier -d replypier -c 'CREATE EXTENSION IF NOT EXISTS vector;'
     (cd "${ROOT}/backend" && "${PYTHON}" -m alembic upgrade head)
     start_process backend "${ROOT}/backend" "${PYTHON}" -m uvicorn app.main:app --host 127.0.0.1 --port 8018
     start_process knowledge "${ROOT}/backend" "${PYTHON}" -m app.workers.run_knowledge_processor