There are multiple ways to do this:
Using Logic Apps with Web/Webhook activity.
Configure a logic app that, upon getting an HTTP request, can send an email to the required set of people for failure. In the pipeline, configure the failure option to hit the URL generated by the logic app.
Using Alerts and Metrics from pipeline options.
We can set up this from the pipeline itself, where we get numerous options for email on any activity failure within the pipeline.
