QUESTION:
Is there a way to know the latest task completion date on the project level?


ANSWER:
You can use standard reports that will provide you that kind of information like ‘task completion’.

The report Task Status Compliance shows the task status information for a selected project and allows the Project Manager to update the status on behalf of a resource.
It selects all active tasks for the project and displays all planned, actual and status information.
It allows to see completed tasks by enabling the checkbox "include completed tasks", this is how you can have needed information.