After cleaning, maybe swap the exhaust with intake (they may be same part number) to see if the code follows.
The fuel pump delivery/driver module is a separate control module that regulates the pulses to the fuel pump (PWM) to control its speed and thus pressure. It gets feedback from the pressure sensor to increase or decrease pulse width.
Here is an example, I do not know if it is used for LPFP, HPFP or both on your vehicle. Or if this is correct for your vehicle.
https://www.ebay.com/itm/16674357263...3ABFBMuO6K5LBk
Also, there were some issues with a high failure rate of HPFPs in certain BMWs around 2011, enough that BMW extended the warranty. That program would have expired by now, but does raise the chances yours went bad and the Amazon replacement is bad right from the box. I hate to even assume such, but the possibility exists.