CB doesn't handle sending emails anymore as we now use Joomla's API for that. Have you made sure Joomla can even send emails? Ensure your Joomla mailer configuration is correct.

If the email is reporting success, but not sending then it's not the API failing. Usually when that happens your mail server is failing to deliver the email. Often due to some sort of anti-spam policy. Try contacting your host to see if they can check the outbound mail logs. Aside from that there's nothing more I can suggest.

Try using Joomla's mass mailer and see if that sends anything. CB is using Joomla API so there isn't any reason CB couldn't send emails if Joomla can. Also be sure you didn't turn CBs emails off in CB > Configuration > Integrations via "Send Emails" parameter.

Unfortunately I don't have anything further to suggest. If it's not throwing any errors then the email is being sent to the mail server, but probably being failed to deliver for whatever reason. Suggest also checking your spam folder as it's possible it's being sent, but being marked as spam. Typically the only reason for emails to just suddenly stop sending is something changed on the server or on the recipient.