Hi,
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You can confirm whether the mails are sent to the outside by checking the mail flow logs of Exchange Server. The specific path is as follows:
D:\Exchange Server 2016\TransportRoles\Logs\Hub\ProtocolLog\SmtpSend
D:\Exchange Server 2016\TransportRoles\Logs\FrontEnd\ProtocolLog\SmtpSend
D:\Exchange Server 2016\TransportRoles\Logs\FrontEnd\ProtocolLog\SmtpReceive
D:\Exchange Server 2016\TransportRoles\Logs\MessageTracking And IIS log
Please feel free to contact me for any updates.And if this helps,don't forget to mark it as an answer.