Hi lukasschäfer,
It should not be related with S32DS. In fact i checked on my side with 12345 project attached and it works fine.
Furthermore - you said the application works to be programmed from the Matlab - this means the UART is operational otherwise the programming would fail.
I would do the following:
#1: configure the Simulink to build the application for SRAM and test if it is the same behavior

#2: After programming try an ATTACH without RESET from S32DS.

What do you see in debugger - is you suspend and resume the target? Does the PC changes?

#3: Do you have a single board ? Does it happens the same on other boards ?
FYI here is my board revision.

#4: Does your USB allows enough current drawn ? Perhaps you can try with an external power source as well to see if the behavior is changing.
Best regards,
Daniel