TDA8571J does not output a signal
After quite some hours of double-checking, overthinking and studying the datasheet the 100th time, I could figure out the solution by myself:
There is a hint in the datasheet on page 8:

Notes

The circuit is DC adjusted at VP= 6 to 18 V and AC operating at VP= 8.5 to 18 V.


I interpret this as &quot;the circuit can only enter operation condition at a Vp of 8.5V or higher&quot; since 8.5V are also needed on the mode pin to enter working condition and I suppose it is not allowed to have a higher voltage than Vp on mode pin.
However I find it still confusing, that in the datasheet it says VpMIN = 6V as well as that the table on page 8 only tells about the mode pin voltages at Vp = 14.4V .
I tried with an extra 12V power source for the TDA8571J and it worked without any problems.