Image pickup apparatus capable of controlling power supply, its control method, and storage medium

An image pickup apparatus attachable to and detachable from an accessory and configured to set a first mode, and a second mode that consumes power less than that of the first mode, the image pickup apparatus comprising:

• a memory storing instructions;
• and
• a processor configured to execute the instructions to:
• control the accessory by communicating with the accessory,
• limit power supply to the accessory in a case where the accessory is in a first state in which the accessory is operated by the power supplied from the image pickup apparatus and the image pickup apparatus is set to the second mode, and
• lift a limitation on the power supply to the accessory in a case where the processor determines that a specific condition is satisfied,
• wherein the accessory is set to either the first state or a second state that is different from the first state,
• wherein in a case where the image pickup apparatus is set to the second mode, the processor is configured to control the power supply to the accessory differently depending on whether the accessory is in the first state or in the second state.