E-Mail Notifications
In the SAP HANA Cloud Central - Alerts application, it isn't possible to setup e-mail notification like in the on-premises version.
The SAP BTP includes a service called the Alert Notification Service that provides a common way for other services or applications running in the SAP BTP to send out notifications such as an e-mail, a post to a Microsoft Teams or Slack channel, the creation of a ticket in ServiceNow, or a webhook to send events to any Internet REST endpoint. The SAP HANA Cloud database and data lake can pass on events to the Alert Notification Service when an alert is triggered.
To setup the SAP BTP Alert Notification Service, follow the steps in the blog Alerts in SAP HANA Database and Data Lake from my colleague Dan van Leeuwen. Link to the Blog: https://developers.sap.com/tutorials/hana-cloud-alerts.html