It is desirable not to send notifications (sms/push notification/webhook) for certain domains if the failure is caused by a DNS problem.
If the name server is not reachable, this message will be sent by SMS: "Reason: unrecoverable error in name resolution". Maybe it is possible to filter on this text.
It is better to create categories with different causes. For each uptime check (or possibly a global setting), you should then be able to set per category (with different causes of a malfunction) whether you want to receive a notification.
Or maybe simpler. One (or more) texts can be set with words. If the cause of the outage contains this text, do not send a notification.