feat: add health check endpoint, fix task date filtering, and update Next.js type reference path

app/api/health/route.ts

@@ -0,0 +1,7 @@
+import { NextResponse } from "next/server";
+
+export const runtime = "edge";
+
+export function GET() {
+  return NextResponse.json({ status: "ok", timestamp: new Date().toISOString() });
+}