Power BI does have the provision for automated anomaly detection as part of a refresh schedule for data, yet it is subjected to vital limitations. The self-contained anomaly detection capabilities are in visuals, always refreshing dynamically along with your data at every instance the dataset gets updated. Setting up alerts or notifications for detected anomalies can be automated but will require an additional configuration.
Here is the way to effectively automate:
Enable scheduled refresh
You need to set a scheduled refresh in the Power BI service so that your dataset will be up to date for updates with a frequency you can choose (every day, every hour, etc.). Once the refresh is triggered, the logic for anomaly detection with the new data will be evaluated.
Surface anomalies in reports
Leverage anomaly-enabled line charts on your dashboards. Such charts will get refreshed each time, display any anomalies found, and do this without further manual adjustment.
Send alerts using workarounds.
Currently, Power BI does not allow sending alerts triggered directly from anomaly detection visuals. You can thus Create measures in DAX that report anomalies (e.g., a case where a value exceeds the threshold or diverges from an average).
Wow. Power BI can create data-driven alerts for KPI visuals or card visuals. It is used in conjunction with Power Automate to trigger messages or emails to be sent and render some workflows when certain thresholds are crossed in a model, thus mimicking an anomaly alert.
Export and analyze tools.
Exporting that visual data via the Power BI REST API or using Power Automate to log results to SharePoint, Excel, or databases will allow for the anomaly to be recorded/logged or otherwise interfaced with other systems.