The problem has been solved!

After days of frustrating and unsuccessful troubleshooting in the bus system, I had to take the case to a specialist.

It turned out to be a short circuit in the multifunction steering wheel (MFL), which disabled the I-bus and therefore interfered with the control signals of the electronics.

I believe this was not a typical E53 issue, and I couldn’t find anything about it online. So I’m documenting it here in the forum now.