Is it the property's responsibility or the power supply bureau's responsibility that the electrical appliances are damaged due to the circuit failure in the residential area?

According to what you said, this kind of thing has no foresight, so it is generally irresponsible. However, if there are long-term problems in the residential lines and the property management company fails to take corresponding rectification measures, it will bear the responsibility for dealing with negligence. The property service agreement should also stipulate the maintenance of relevant equipment and facilities, which can be analyzed with reference to specific conditions. You can also give these equipment to the power supply company for maintenance, and then the power supply company is responsible for maintenance.