You will need to create a field called [Date Delivered] to capture the date that the Status was changed to delivered.
One way to do that is when a form rule
When the record is saved
and condition
Status has changed to Delivered
Action
Change the value in the field [Date Delivered] to "the current date"
The you would change your formula for days overdue to something like this.
If(
[Status] = "Delivered"
and [Date Delivered] >= ToDate([Calculated Finish Date]),
ToDays([Date Delivered] - ToDate([Calculated Finish Date])),
Max(0, ToDays(Today() - ToDate([Calculated Finish Date]))))
A form rule will only work if you are editing record one by one on a form. If you intend to do Grid Edit, then you would need to use an automation or Action to update the [Date Delivered]
