Do you mean that your mailbox could send OOF to external mailbox successfully? Does the external account you used belong to the same domain(such as, gmail or hotmail) as the single user?
If your mailbox cannot send OOF to external mailbox successfully, I would suggest you have a check settings with remote domain:
If your mailbox could send OOF to that external domain, I would suggest you use command below to check whether OOF generate for that single user:
Get-MessageTrace -SenderAddress singleUser@domain.onmicrosoft.com -StartDate 3/21/2021 -EndDate 3/23/2021
If this OOF generated and delivered, this OOF message may be blocked on the recipient side.
If OOF email doesn't generate, it means there may exist issue with the OOF configuration on this single user, I would suggest you try to check from OWA for this mailbox:
If all settings configured correctly, I would suggest you open a service request to Office 365 to let them help you check from the back-end.
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