Hi guys, I could dive a little deeper into the topic.
FT-Prog seems to clear the user area of the EEPROM, which seem to hold digilent-specific additional and necessary info.
I could write the user area content of a working CMOD-A7 to the user area of the non-working, which finally fixed the problem.
https://www.ftdichip.com/Documents/AppNotes/AN_121_FTDI_Device_EEPROM_User_Area_Usage.pdf
Thanks anyway for anyone who considered to help me.