Hi BetterHQ,
Unfortunately, you can’t mark an appointment as completed in outlook and sync status to the dynamics.
As you mentioned, there is no OOB button to mark an appointment as complete on the Outlook appointment window
Through my search, I found following link, which provides one way to mark appointments as completed through categories.
How to mark calendar appointment as complete in Outlook? (extendoffice.com)
but they are only used to easily distinguish between a large number of items, they can’t sync status of appointments from outlook to dynamics.
Go Settings > Administrator > System Settings > Synchronization tab to click Synchronization fields link.

Contrast the two entities of Appointment and task, you can find that the status field does not appear in the Appointment.

Which is by-design, status field of appointment doesn’t exists in the Synchronization fields, so you can’t sync status of appointments from outlook to dynamics.
Regards,
Leah Ju
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