As far as I know DNS and NTP servers are hardcoded in HA OS.
I use healthchecks.io and setup a REST sensor in HA that pings the healthchecks.io URL every minute. In healtchecks.io I configured it to send me a Whatsapp and an E-Mail when the ping didn’r hapoen for 5 minutes. Works perfectly fine. But I have to say that my system never had any unplanned downtime in the last 3+ years.