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/message-reasoning.tsx

@@ -0,0 +1,37 @@
+"use client";
+
+import { useEffect, useState } from "react";
+import {
+  Reasoning,
+  ReasoningContent,
+  ReasoningTrigger,
+} from "../ai-elements/reasoning";
+
+type MessageReasoningProps = {
+  isLoading: boolean;
+  reasoning: string;
+};
+
+export function MessageReasoning({
+  isLoading,
+  reasoning,
+}: MessageReasoningProps) {
+  const [hasBeenStreaming, setHasBeenStreaming] = useState(isLoading);
+
+  useEffect(() => {
+    if (isLoading) {
+      setHasBeenStreaming(true);
+    }
+  }, [isLoading]);
+
+  return (
+    <Reasoning
+      data-testid="message-reasoning"
+      defaultOpen={hasBeenStreaming}
+      isStreaming={isLoading}
+    >
+      <ReasoningTrigger />
+      <ReasoningContent>{reasoning}</ReasoningContent>
+    </Reasoning>
+  );
+}