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/ui/input.tsx

@@ -0,0 +1,19 @@
+import * as React from "react"
+
+import { cn } from "@/lib/utils"
+
+function Input({ className, type, ...props }: React.ComponentProps<"input">) {
+  return (
+    <input
+      type={type}
+      data-slot="input"
+      className={cn(
+        "h-9 w-full min-w-0 rounded-4xl border border-input bg-input/30 px-3 py-1 text-base transition-colors outline-none file:inline-flex file:h-7 file:border-0 file:bg-transparent file:text-sm file:font-medium file:text-foreground placeholder:text-muted-foreground focus-visible:border-ring focus-visible:ring-[3px] focus-visible:ring-ring/50 disabled:pointer-events-none disabled:cursor-not-allowed disabled:opacity-50 aria-invalid:border-destructive aria-invalid:ring-[3px] aria-invalid:ring-destructive/20 md:text-sm dark:aria-invalid:border-destructive/50 dark:aria-invalid:ring-destructive/40",
+        className
+      )}
+      {...props}
+    />
+  )
+}
+
+export { Input }