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

components/chat/sign-out-form.tsx

@@ -0,0 +1,25 @@
+import Form from "next/form";
+
+import { signOut } from "@/app/(auth)/auth";
+
+export const SignOutForm = () => {
+  return (
+    <Form
+      action={async () => {
+        "use server";
+
+        await signOut({
+          redirectTo: "/",
+        });
+      }}
+      className="w-full"
+    >
+      <button
+        className="w-full px-1 py-0.5 text-left text-red-500"
+        type="submit"
+      >
+        Sign out
+      </button>
+    </Form>
+  );
+};