Help with alerts in Power Bi Service

Hi Jmrc16 ,

Thanks for raising this, I verified the behavior and updated links so you can follow the official guidance directly. The main tenant level controls for Fabric and Power BI are documented on the tenant settings overview and the tenant settings index which describe what tenant settings can and cannot block for users, including the limited scope of data alerts at the tenant level.
About tenant settings - Microsoft Fabric | Microsoft Learn

For details on how alerts behave for end users and how to manage alerts in the Power BI service see the Set data alerts in the Power BI service article.
https://learn.microsoft.com/en-us/power-bi/create-reports/service-set-data-alerts

The email suggestions you see are produced by Microsoft 365 and Azure Active Directory directory and privacy features rather than by Power BI itself, so review the Microsoft 365 privacy controls documentation and the External collaboration settings for Microsoft Entra documentation to understand how directory visibility and suggestion behavior can be limited.

Overview of privacy controls for Microsoft 365 Apps for enterprise - Microsoft 365 Apps | Microsoft Learn

If you want to request a product change to allow full suppression of alerts or email suggestions, the Fabric Ideas forum is the place to submit and vote on that feedback. 
http://community.fabric.microsoft.com/t5/Fabric-Ideas/ct-p/fbc_ideas

If you would like, I can craft a short forum post using these links that explains the current limitation and recommended mitigation steps for administrators.

Thank you.