When the envelope is not sent to the recipient as an email notification, you should check the below items:

1. Check the status of the envelope. If the status is set as "created," the envelope won't be sent. You should set the status of the envelope as "sent" to send the envelope to the recipient.

2. Check whether you created the envelope as an embedded signing. If you define the clientUserId in the recipient object of the createEnvelope API, the email notification won't be sent. Instead, you should call CreateRecipientView API to get the URL to open the signing page. More information about embedded signing is here: https://developers.docusign.com/docs/esign-rest-api/esign101/concepts/embedding/
If you want to send the email notification to the recipient, please remove the clientUserId under the recipient object of the createEnvelope API call.

3. Check the recipient's email notification.
Log in to the Docusign Portal with the recipient user and click the icon on the top right > My Preferences > Notifications. Under Recipient Notifications, enable "I have an envelope to sign" and click the save button. Then, send the envelope again to the user via API to check whether the email notification is sent to this user.