Is continuing to work and observe a manager's wrongful practices considered participation in sin, even if these practices are not within my job responsibilities?

Your duty towards a negligent manager is to advise him gently and wisely, reminding him of the trust (amanah) and its weight, unless you incur significant harm. If he does not desist, inform whoever can restrain him, if there is benefit in doing so. If you do this, you bear no sin for his actions. And you are not obligated to leave your job as long as you perform your duties without shortcomings.