Hi KyleXu, please find the below answers
Whether those mailbox in the same organization?: yes mailboxes are same organization
Whether emails that sent to Exchange on-premises was read or moved to another folder? No
Whether there exist emails in recipient mailbox which said Exchange online mailbox try to recall this emails? yes
Make sure both mailboxes configured in Outlook and Outlook in running. yes
Make sure Exchange 2016/2019 mailbox could send emails to Exchange online mailbox successfully. yes