What is the difference between the ruling on the act of assigning tasks to employees in a mixed-gender work environment and the ruling on transporting women to a mixed-gender school, given that the original purpose in both cases is permissible?

The previous answers do not include a prohibition of your work. The fatwa from which you understood the prohibition is conditional upon the employee actively seeking to appoint and employ unveiled women in places of forbidden mixing, as this constitutes aiding in sin. However, if the work is merely processing procedures and organizing papers, and the employee does not have the authority to choose applicants or arrange their workplaces, then there is no prohibition in that. The employee should enjoin good and forbid evil and strive to remove objectionable matters to the best of their ability and in accordance with Islamic regulations.