Dear Sarah,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
Per the description shared, I would like to summarize your concern i.e., you are receiving the Notifications when you have published the news in the SharePoint Online site but the users who follow the site isn't receiving the notification.
As per my research, the notifications will be received to the users based on the relevancy:
So, can I know whether the user is not receiving an email from specific SharePoint Online or all SharePoint Online sites? Does this problem happens with the other users who is following the SharePoint Online site?
Thanks for your cooperation.
Sincerely,
Mia | Microsoft Community Moderator