AVF PD in A6 sometimes fails to start, first registration 10/2003

Hello,
After spending several hours searching and reading through various resources, my first question is:
The AVF engine in an Audi A6 with an automatic transmission sometimes fails to start.
"The following is a description of the situation:"
When the ignition is turned on, the ESP and ABS lights flash. Additionally, the illumination of the automatic transmission indicator (R, N, P, etc.) is reversed; what is normally lit is now dark, and what is normally dark is now lit. In this state, the engine starts, but does not turn over. After repeatedly turning the ignition on and off, the lighting returned to normal, and the engine started again.
"When I leave the ignition on, the lighting eventually switches back on and the car starts. Strangely, I have the feeling that this only happens when the gear selector is in the 'P' position and not in 'N'. However, I haven't tried 'N' enough times to be sure. Sometimes it stays quiet for hours, and sometimes it happens more frequently in a row. It started harmlessly, but now it's happening more and more often, even several times a day." It doesn't matter whether the engine is warm or cold.
When it's running, everything is fine; it doesn't stop working and it doesn't just freeze.

Here's what I've tried so far:
Ignition switch replaced.
Charging voltage measured: 14 volts, resting voltage measured: 12.1 volts.
Battery replaced. 100AH, 760A cold cranking current.
Tried the second key.
Error codes read:
The engine electronics are reporting an error with the EGR valve, exceeding the control limit... I don't think that's related.
Transmission control reports: 1757 Battery voltage interruption and 1850 CAN data bus: missing message from the engine control unit.

The battery voltage interruption was already present before the battery was replaced, and after the replacement, the error didn't reappear initially.

ABS/ESP reports: I also encountered an error related to the CAN data bus, but unfortunately, I didn't write it down because it didn't seem important at the time.
Now I see that everything seems to be interconnected and that there must be an origin.

Is there a power relay that supplies power to the motor control unit, ESP, ABS, and transmission control unit? Could this be related to, or even integrated with, the preheating relay?

Could the combination of instruments be the cause of the problem? Are combination ovens prone to circuit board failures?

Or could it be coming from the transmission? There's probably a switch integrated there for the selected gear, and it might be generating incorrect values.

There are many questions, but I'm not really sure how to proceed at the moment.
Otherwise, he drives completely normally, with no differences from before, and there's no lack of power.

Thank you for your help. Best regards, André.