Initial commit: EGBE chatbot template

Stripped from vercel/chatbot (Apache 2.0):
- Dropped @vercel/* packages and AI Gateway
- Removed artifacts feature (code/text/sheet/image side panel)
- Switched AI provider to @ai-sdk/openai-compatible -> EGBE LiteLLM
- Replaced Vercel Blob upload with data URLs
- Dropped Redis resumable streams and rate limiter (in-memory now)
- Added Dockerfile (Next.js standalone) + entrypoint that runs migrations
- Wired DATABASE_URL, EGBE_AI_API_URL/KEY, NEXT_PUBLIC_BASE_URL for app-deploy.sh

app/(auth)/layout.tsx

@@ -0,0 +1,43 @@
+import { ArrowLeftIcon } from "lucide-react";
+import Link from "next/link";
+import { SparklesIcon, VercelIcon } from "@/components/chat/icons";
+import { Preview } from "@/components/chat/preview";
+
+export default function AuthLayout({
+  children,
+}: {
+  children: React.ReactNode;
+}) {
+  return (
+    <div className="flex h-dvh w-screen bg-sidebar">
+      <div className="flex w-full flex-col bg-background p-8 xl:w-[600px] xl:shrink-0 xl:rounded-r-2xl xl:border-r xl:border-border/40 md:p-16">
+        <Link
+          className="flex w-fit items-center gap-1.5 text-[13px] text-muted-foreground transition-colors hover:text-foreground"
+          href="/"
+        >
+          <ArrowLeftIcon className="size-3.5" />
+          Back
+        </Link>
+        <div className="mx-auto flex w-full max-w-md flex-1 flex-col justify-center gap-10">
+          <div className="flex flex-col gap-2">
+            <div className="mb-2 flex size-9 items-center justify-center rounded-lg bg-muted/60 text-muted-foreground ring-1 ring-border/50">
+              <SparklesIcon size={14} />
+            </div>
+            {children}
+          </div>
+        </div>
+      </div>
+
+      <div className="hidden flex-1 flex-col overflow-hidden pl-12 xl:flex">
+        <div className="flex items-center gap-1.5 pt-8 text-[13px] text-muted-foreground/50">
+          Powered by
+          <VercelIcon size={14} />
+          <span className="font-medium text-muted-foreground">AI Gateway</span>
+        </div>
+        <div className="flex-1 pt-4">
+          <Preview />
+        </div>
+      </div>
+    </div>
+  );
+}