Are the extra hours granted for staying after official work hours considered permissible, knowing that there is no actual work in the evening except in emergencies, and that I perform additional work in the morning to compensate for staff shortages?

If your manager is authorized to act on this, then there is no harm for you in accepting the bonus and benefiting from it. But if he is not authorized, then it is not permissible for you to accept it. You have the right to refuse extra work unless a bonus is specified for you as compensation for it.