Is it permissible to remain at work and receive pay for overtime hours during which no actual work is done, knowing that colleagues do so and the direct manager approves of it?

It is permissible to benefit from overtime hours and receive payment for them if it is in accordance with the employer's regulations or at the direction of the responsible party, even if no actual work is performed; because the wage is established by enablement (tamkeen). If the work system does not grant you the right to those hours when they are not needed, then it is not permissible to benefit from them. You must adhere to the agreed-upon working hours, and it is not permissible to leave before their end except with the employer's permission, because the employee is a private hire (ajeer khass) and his benefit (manfa'ah) is owned by the hirer throughout the working hours, and you are entitled to your salary by your presence at the workplace and your adherence to it, even if there is no work.