Is it permissible for a dentist working in the government sector, for whom the medical administration provides only extraction tools, to provide tools for dental fillings and prosthetics at his own expense and receive payment for them directly from patients during official working hours and with the knowledge of his direct manager?

It is not permissible for an employee to work for anyone other than their employer during work hours. Your performing of fillings or prosthetic work necessitates the use of work tools for your personal benefit, which is forbidden. Furthermore, it occupies time and delays patients who are scheduled for extractions. This action exposes you to accountability for exploiting work time and tools. The approval of the direct manager is irrelevant, as he does not have the authority to grant it.