@Adam Black that's a good question. We're using PagerDuty to handle service requests and it integrates with Azure just fine. Even though you may not use it, it's just an example... you can still configure service health alerts with respective webhooks and automate the entire flow as you need. Our flow is simple, if there is a service outage, we receive a notification to PagerDuty (via configured webhook in Azure Service Health), see more here: https://docs.microsoft.com/en-us/azure/service-health/alerts-activity-log-service-notifications-port... Then, we acknowledge the issue and send an email note to all staff about the problem. For that, you may want to create an AD group called 'Staff/All staff', etc.
There are more complex automated scenarios that involve Azure PowerApps, Microsoft Power Automate, or services combination (+ some coding). There are multiple templates you can use as a basis from here: https://flow.microsoft.com/en-us/templates/
Here's the sample that does something similar with Logic Apps: https://github.com/Azure/azure-quickstart-templates/tree/master/201-alert-to-text-message-with-logic... Most people are very sensitive about the SMS messages, so we stick to email notifications to a specific 'all staff' user group in AD.
In case you badly need to send SMS messages, this scenario may require some development. Still, to achieve that we need a webhook from Azure Service Health alert, then, you need to assemble Azure Function that will be using it as a trigger: https://www.twilio.com/blog/2017/01/how-to-send-daily-sms-reminders-using-c-azure-functions-and-twil... Then, to get the users from the AD, you may want to use Graph API as described here (https://dhendry.wordpress.com/2016/02/26/azure-ad-retrieving-group-members/), and finally, iterating over the users' profiles, you should be able to send SMS messages with Twilio (or using .NET native tools + O365 PTSN setup).
As you can see, scenarios are different, but they should give you some food for thought 