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

e2e/services/customer-site/server.ts

@@ -1,11 +1,11 @@
-// A pretend customer website with the ChatterMate widget embedded the way the
+// A pretend customer website with the ReplyPier widget embedded the way the
 // dashboard's install snippet does it. Everything about the embed comes from the
 // query string:
 //
 //   http://127.0.0.1:13000/?widget=<id>
-//     &config=<json>   → window.chattermateConfig (launcher, position, trigger, …)
-//     &token=<jwt>     → window.chattermateToken (token-authenticated widgets)
-//     &trigger=1       → adds a page button with data-chattermate-open
+//     &config=<json>   → window.replypierConfig (launcher, position, trigger, …)
+//     &token=<jwt>     → window.replypierToken (token-authenticated widgets)
+//     &trigger=1       → adds a page button with data-replypier-open
 //     &snippet=iframe  → the dashboard's iframe snippet instead of the script
 //
 // It has to be a real server on 127.0.0.1: Chrome's Local Network Access check
@@ -23,7 +23,7 @@ function arg(name: string, fallback: string): string {
 
 const port = Number(arg('port', '13000'))
 const apiUrl = arg('api', 'http://127.0.0.1:18000/api/v1')
-const loaderUrl = arg('loader', 'http://127.0.0.1:15173/webclient/chattermate.min.js')
+const loaderUrl = arg('loader', 'http://127.0.0.1:15173/webclient/replypier.min.js')
 
 interface Embed {
   widgetId: string
@@ -36,7 +36,7 @@ interface Embed {
 /** The dashboard's iframe snippet (AgentWidgetTab), classed so the page object finds it. */
 function iframeSnippet(widgetId: string): string {
   const src = `${apiUrl}/widgets/${encodeURIComponent(widgetId)}/data`
-  return `<iframe class="chattermate-iframe" src="${src}" width="100%" height="600" frameborder="0" title="AI Assistant" allow="clipboard-write"></iframe>`
+  return `<iframe class="replypier-iframe" src="${src}" width="100%" height="600" frameborder="0" title="AI Assistant" allow="clipboard-write"></iframe>`
 }
 
 function page(embed: Embed): string {
@@ -51,18 +51,18 @@ function page(embed: Embed): string {
 </html>`
   }
   const globals = [
-    `window.chattermateId = ${JSON.stringify(embed.widgetId)};`,
-    `window.chattermateBaseUrl = ${JSON.stringify(apiUrl)};`,
+    `window.replypierId = ${JSON.stringify(embed.widgetId)};`,
+    `window.replypierBaseUrl = ${JSON.stringify(apiUrl)};`,
     // config arrives as JSON text; parse it here so a malformed value fails the request, not the page.
-    embed.config ? `window.chattermateConfig = ${JSON.stringify(JSON.parse(embed.config))};` : '',
-    embed.token ? `window.chattermateToken = ${JSON.stringify(embed.token)};` : '',
+    embed.config ? `window.replypierConfig = ${JSON.stringify(JSON.parse(embed.config))};` : '',
+    embed.token ? `window.replypierToken = ${JSON.stringify(embed.token)};` : '',
   ].filter(Boolean).join('\n      ')
   return `<!doctype html>
 <html lang="en">
   <head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1"><title>Acme Store</title></head>
   <body>
     <h1>Acme Store</h1>
-    ${embed.trigger ? '<button type="button" data-chattermate-open>Chat with us</button>' : ''}
+    ${embed.trigger ? '<button type="button" data-replypier-open>Chat with us</button>' : ''}
     <script>
       ${globals}
     </script>