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

frontend/scripts/build-webclient-dev.ts

@@ -23,18 +23,18 @@ async function buildWebClientDev() {
     process.env.NODE_ENV = 'development'
     
     // Baked DEFAULT base URL only; getBaseUrl() still resolves
-    // window.chattermateBaseUrl / window.APP_CONFIG at runtime, so no rebuild is
+    // window.replypierBaseUrl / window.APP_CONFIG at runtime, so no rebuild is
     // needed when a deployment's env changes.
     const apiUrl = process.env.VITE_API_URL || 'http://localhost:8000/api/v1'
     console.log('Using API URL:', apiUrl)
 
-    const sourceFile = resolve(dirname(__dirname), 'src/webclient/chattermate.js')
+    const sourceFile = resolve(dirname(__dirname), 'src/webclient/replypier.js')
 
     await build({
       entryPoints: [sourceFile],
       bundle: true,
       minify: false, // Don't minify for development
-      outfile: resolve(dirname(__dirname), 'public/webclient/chattermate.min.js'),
+      outfile: resolve(dirname(__dirname), 'public/webclient/replypier.min.js'),
       format: 'iife',
       target: ['es2015'],
       loader: {
@@ -42,17 +42,17 @@ async function buildWebClientDev() {
       },
       define: {
         'process.env.NODE_ENV': '"development"',
-        '__CHATTERMATE_API_URL__': JSON.stringify(apiUrl),
+        '__REPLYPIER_API_URL__': JSON.stringify(apiUrl),
       },
       sourcemap: true, // Add sourcemap for development
     })
 
     // Copy output to dist/webclient directory
-    const publicWebclientPath = resolve(dirname(__dirname), 'public/webclient/chattermate.min.js')
-    const publicSourcemapPath = resolve(dirname(__dirname), 'public/webclient/chattermate.min.js.map')
+    const publicWebclientPath = resolve(dirname(__dirname), 'public/webclient/replypier.min.js')
+    const publicSourcemapPath = resolve(dirname(__dirname), 'public/webclient/replypier.min.js.map')
     const distWebclientDir = resolve(dirname(__dirname), 'dist/webclient')
-    const distWebclientPath = resolve(distWebclientDir, 'chattermate.min.js')
-    const distSourcemapPath = resolve(distWebclientDir, 'chattermate.min.js.map')
+    const distWebclientPath = resolve(distWebclientDir, 'replypier.min.js')
+    const distSourcemapPath = resolve(distWebclientDir, 'replypier.min.js.map')
     
     // Ensure dist/webclient directory exists
     if (!fs.existsSync(distWebclientDir)) {