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

hooks/use-messages.tsx

@@ -0,0 +1,39 @@
+import type { UseChatHelpers } from "@ai-sdk/react";
+import { useEffect, useState } from "react";
+import type { ChatMessage } from "@/lib/types";
+import { useScrollToBottom } from "./use-scroll-to-bottom";
+
+export function useMessages({
+  status,
+}: {
+  status: UseChatHelpers<ChatMessage>["status"];
+}) {
+  const {
+    containerRef,
+    endRef,
+    isAtBottom,
+    scrollToBottom,
+    onViewportEnter,
+    onViewportLeave,
+    reset,
+  } = useScrollToBottom();
+
+  const [hasSentMessage, setHasSentMessage] = useState(false);
+
+  useEffect(() => {
+    if (status === "submitted") {
+      setHasSentMessage(true);
+    }
+  }, [status]);
+
+  return {
+    containerRef,
+    endRef,
+    isAtBottom,
+    scrollToBottom,
+    onViewportEnter,
+    onViewportLeave,
+    hasSentMessage,
+    reset,
+  };
+}