If you are experiencing an issue with email notifications, first of all, make sure that you're checking the right email inbox. It should be the same as the one in the My Email for Notifications field shown in the screenshot.
If that's the case, check your Spam folder for notifications from Manychat — they could have gotten there by mistake.
Also, ensure you're selected as a team member who should receive notifications in the Notify Assignees action in your automation.