Salesforce Case Feed Notifications and Emails in Experience Cloud Site

On an Experience Cloud site, when a user responds to a case, the owner will be notified but not any other people who have access to the case. It is important that the "notify owner of case comments" is selected to ensure the owner gets notified. Now, the only way for other users to receive a notification when a Chatter post is performed, is to create a Flow that sends email notifications to the users that are not the owners. 

When the owner again responds via a comment, the user who responded to their post may receive an email and notification depending on how they configured their personal settings. See Guidelines for Managing Your Personal Chatter Email Settings for more details.