Your nameservers and DNS is fine. Your origin web server though, is not. The “Service Unavailable” / 503 response you get is returned by your origin web server.
An “Error 503: Service Unavailable” with no Cloudflare in the message means you need to contact your hosting provider for assistance.
Some of my requests got 503 Service unavailable, and some got 524 Timeout, something is wrong with your origin web server, possibly overloaded. If you were using shared/managed hosting, I would reach out to them for more help.