In order to send emails after an update, the certificate needs to be configured in exchange online to allow the server to server authentication to work. The following is a guide to go about this:

Connect Dynamics 365 Customer Engagement (on-premises) to Exchange Online

If updating a certificate, only the commands need to be run. No email profile configuration need be done. Only the section specified in the link below:

Connect Dynamics 365 Customer Engagement (on-premises) to Exchange Online

These commands can/should be run on the deployment server