Give students the ability to mark homework as completed. Literally all UK MIS' or learning platforms give students this feature.

The teacher can override the completion if it has not been completed or needs redoing.

The Learning Task page would then be split into "Upcoming", "Completed", "Overdue"; when a student marks a homework as completed, it moves from upcoming to completed. If the student does not mark it off before the due date, it becomes overdue.

Also, stop categorising the Learning Tasks page by subject. Categorise it by closest due date first, irrespective of subject. This gives the student an overview of tasks that need to be completed first.

If you want a good example of this suggestion in action, look up the Microsoft Teams assignment feature. This shows my suggestion in practice!