Do you have a pull-up resistor on the CS pin? (the schematic snippet you shared does not include it)
If you refer to the power-up/down section of the datasheet you'll see that the CS must always follow VCC on power-up/down. Failure to do so can result in an unknown power-up state, and even though you can typical reset the flash memory though software reset, I've observed issues in the past when I forgot that pull-up myself.
Further assuming that you are putting the entire circuit in sleep mode, you need to make sure that the GPIO pin of the MCU is not floating that CS pin, it needs to be held high during the sleep mode.
If you don't have the pull-up, I'd suggest adding it and retesting the power consumption.