Currently, there is no dedicated button or status to mark a published shift as completed.
However, you can follow this workaround to indicate that the work is done and to prevent others from duplicating the task:
Once finished, the employee should clock out of their assigned shift via the QuickBooks Workforce app. This automatically creates a timesheet entry linked to that specific shift.
After clocking out, the employee can submit their time to confirm all assigned work is complete.
If you are the admin, go to All Apps > Time > Approvals, then approve and lock the time to ensure no one else can edit or repeat the task.
For more details, check out this article: Manage shifts for QuickBooks Time web.
Keep us posted if you need anything else.