Is working for a company that demands undue money from employees of government entities in exchange for free training courses considered participation in sin, and is the resulting salary forbidden? And what is the way to atone for this sin?

If the courses are free and the company is not entitled to take money from employees, then what you are doing is not permissible for you, nor does it override your manager's command, due to the Almighty's saying: "And do not cooperate in sin and aggression." You must repent and refrain from this work, and demand that the company return the money to its owners, otherwise you must inform the employees of the truth. As for your salary, if it is for permissible work, then it is permissible. But if it is in exchange for forbidden work, then it is forbidden money that you must spend on general Muslim welfare, unless you are poor, in which case you may take from it what suffices your needs.