Azure Monitor for Virtual Machines will monitor local ports on a VM from within the OS, monitoring inbound and outbound traffic.
Depending on your need you can use Application Insights URL ping tests, Standard tests, or Connection monitor for URL monitoring.
SQL insights can be used for monitoring SQL databases on VM's as well.
All of this can be alerted on in using Log Alerts, though some (like connection monitor and the URL tests) build the alerts as part of the deployment wizard.