Is working in a government job that includes long periods without tasks considered forbidden (haram), especially if the manager allows leaving without registering it as leave?

There is no objection to your remaining idle during working hours as long as you have not been assigned any task, for a private employee's full entitlement to wages is by making himself available to the employer, whether he is assigned work or not. Similarly, there is no objection to leaving when there is no work, provided the authorized manager grants permission.