Question:

Why are notification emails not being sent when a Survey is published using the Multichannel (MC) Engine?

Answer:

This is working as designed. Notification emails are not sent to the publisher when the MC Engine is used for publishing.

To verify whether Survey publishing is being handled by the MC Engine, check the Survey Publish Apex setting in Veeva Settings and confirm that the Survey Publish Apex is set to 1. 

Example:

Related Documentation:

CRM Help Documentation: Publishing a Survey