I will provide an honest answer. I trust this will be appreciated. Please remember that a low rating PUNISHES me for being honest and that I receive nothing for my time until a positive rating is clicked.
the fan runs based on coolant temperature and pressure in the ac system then based on a variable speed controller internal to the fan.
it has constant voltage so correcting voltage wont help, and this has nothing to do with the resistor you replaced.
most likely one of the two sensors (pressure and temp) is sending the wrong signal causing the car's computer to trigger high speed fan running all of the time, however, there is a slight chance the issue is also internal to the fan's speed controller.
the cause can be verified with a factory BMW scan tool which can monitor all inputs and outputs from all systems. I assume this this testing has not been carried out.
if you would like to avoid guesswork on this, you will need to invest in this type of diagnostic
Please let me know if you have further questions. Please do not forget to click a positive rating as this is the only way I receive credit for my answer, thank you. Best wishes with your vehicle.