The SharePoint mobile app sends a push notification when news that may be interesting to you is posted.
The app determines if a news post is interesting to you based on your relationship with the person who posted the news. The following may suggest interest:
Do the two of you work closely together, based on common work in Microsoft 365?
Is the person who posted the news in your management chain?
Do you work closely with people who report to the person who posted the news?
Information about managers depends on your organization's directory which can be updated in Azure Active Directory.
The way interest in news is determined will change over time. This article will be updated when changes are made.