You essentially have 2 options and they vary in terms of speed and time necessary to develop them:
Custom Journey Builder Activity (as suggested by zuzannamj)
This is by far the most proper approach and will give you the most flexibility and calls being executed as close to real-time as possible in Marketing Cloud, but it does require resources and time to ...
The answer is NO. There is no way to add an email to the notification settings of an automation.
Actually, there is an option in the Soap request on the help page that "normally" adds this parameter, but under a comment that clearly stats that it does not work: Check out the comment on the Notifications tag
<!--<Notifications> DOES NOT WORK
This can only be achieved using Custom Activity in Journey Builder. You will need to install a Managed Package in Marketing Cloud, build the activity and host it on a web server.
The whole setup is explained in the documentation: Build Custom Activities and Events
A working knowledge of RequireJS for dependency management
You can definitely send Bell Notifications via apex. Andrew Fawcett explained this feature in detail in his article https://andyinthecloud.com/2019/06/30/getting-your-users-attention-with-custom-notifications/.
A month ago I had a task to send a notification to my user when deletion of test data is finished. This is an example code how it was done:
The Enable Salesforce Notification Banner is a Global banner (rectangle) that shows in all pages that usually displays Salesforce communications.
What you are looking for is the App Notifications: https://developer.salesforce.com/docs/atlas.en-us.salesforce1appadmin.meta/salesforce1appadmin/s1_admin_guide_notifications.htm
Setup --> Apps --> Mobile Apps -...
This is how the standard functionality works with notifications and the bell.
You'd be better off using some sort of "Today's Tasks" component on a home page than relying on the bell.
I know this may be a little late, but for all those who are still looking for implementation custom notification(Bell notification) via Apex:
The way you solve this requirement is to create an Object called "Custom_Push_Notification__c" with few fields mentioned in below blog link. Once record is inserted into this object, custom notification will be ...