There may be times a domain is added and created email accounts send email but the recipient never receives the email.
You will want to check the Exim logs to see what specifically happened to the email. Let's say you sent the email from this fake email address as an example; email@example.com
exigrep firstname.lastname@example.org /var/log/exim_mainlog
It may look something like this.
[05:14:36 cphs01 root@94301956 ~]cPs# exigrep email@example.com /var/log/exim_mainlog
2021-03-09 05:10:02 1lJZJO-0006Hh-HW H=(myserver.domain.com) [::1]:43625 Warning: "SpamAssassin as cpaneleximscanner detected OUTGOING smtp message as NOT spam (-1.0)"
2021-03-09 05:10:02 1lJZJO-0006Hh-HW <= firstname.lastname@example.org H=(myserver.domain.com) [::1]:43625 P=esmtpa A=dovecot_login:email@example.com S=682 firstname.lastname@example.org T="this is a test I" for email@example.com
2021-03-09 05:10:02 1lJZJO-0006Hh-HW Sender identification U=lalichet D=domain.com Sfirstname.lastname@example.org
2021-03-09 05:10:02 1lJZJO-0006Hh-HW SMTP connection outbound 1615284602 1lJZJO-0006Hh-HW domain.com email@example.com
2021-03-09 05:10:06 1lJZJO-0006Hh-HW => firstname.lastname@example.org R=dkim_lookuphost T=dkim_remote_smtp H=remoteserver.domain.com [192.168.1.254] X=TLS1.2:ECDHE-RSA-AES256-GCM-SHA384:256 CV=yes C="250 OK id=1lJZJO-0003dQ-7I"
2021-03-09 05:10:06 1lJZJO-0006Hh-HW Completed
The last line completed states the email transaction ended but the line before it shows to what email server the email was routed. In this case, the email was sent to remoteserver.domain.com instead of the gmail mail servers.
[root@cptestvm ~]# dig mx +short gmail.com
This means the email was delivered but Exim is configured with something called a smarthost to relay email to another mail server and then the email is relayed from there. At this point, it would be that mail server that needs to be checked to determine why that domain's email is not being routed to the next mail server for delivery.
There is no way to work around this except to remove the smarthost but it would be better to begin troubleshooting on the mail server being used as a smarthost.