Make sure the Notification plugin and all the extensions are up-to-date!
The Recipients field is empty
Notification v7 uses WordPress' REST API to render the recipients field. You must ensure the /notification endpoint is accessible and the API is accessible.
Nothing is sent
To debug the missing message (Carrier execution) please enable the Notification log in Notification > Settings > Debugging. All the executions will be caught there.
If the notification gets caught, you can inspect the details (ie. if the recipient is set correctly) and if they seem to be ok, check if your WordPress is sending the emails (SMTP is set correctly?) or it can connect to the API (depends on the selected Carrier).
Most of the time this is caused by the post editor saving the content multiple times. Ie. Gutenberg saves the main content in one request, taxonomy terms in another request, ACF saves the fields in another request, and so on.
The Notification plugin already has some editor integrations implemented, but if it still sends double notifications in your case, you may try to use the Notification : Prevent Duplicates extension.
Cannot see the Custom Post Type on the Triggers list while creating a Notification